Question 1200395
<font color=black size=3>
I'll go over two methods with these types of problems.


Method 1


Start at "-6" on the number line.
Move 6 units to the right to arrive at "0".
Move another 2 units to arrive at "2". 
We have traveled 6+2 = 8 units total to the right.


Then from the location "2" on the number line, move 2 units left to get back to "0". 
Move another 13 units to the left (so you move 2+13 = 15 units total to the left) to arrive at <font color=red>-13</font> which is the final answer.


Refer to the diagram below.
We start at A = -6
Then move to B = 2 (moving 8 units to the right)
Then move to C = -13 (moving 15 units to the left)
{{{
drawing(600, 200, -16,5,-5,5,
line(-15-3,0,4+3,0),
line(-15,0.2,-15,-0.2),
line(-14,0.2,-14,-0.2),
line(-13,0.2,-13,-0.2),
line(-12,0.2,-12,-0.2),
line(-11,0.2,-11,-0.2),
line(-10,0.2,-10,-0.2),
line(-9,0.2,-9,-0.2),
line(-8,0.2,-8,-0.2),
line(-7,0.2,-7,-0.2),
line(-6,0.2,-6,-0.2),
line(-5,0.2,-5,-0.2),
line(-4,0.2,-4,-0.2),
line(-3,0.2,-3,-0.2),
line(-2,0.2,-2,-0.2),
line(-1,0.2,-1,-0.2),
line(0,0.2,0,-0.2),
line(1,0.2,1,-0.2),
line(2,0.2,2,-0.2),
line(3,0.2,3,-0.2),
line(4,0.2,4,-0.2),
locate(-15.5,-0.2,"-15"),
locate(-14.5,-0.2,"-14"),
locate(-13.5,-0.2,"-13"),
locate(-12.5,-0.2,"-12"),
locate(-11.5,-0.2,"-11"),
locate(-10.5,-0.2,"-10"),
locate(-9.2,-0.2,"-9"),
locate(-8.2,-0.2,"-8"),
locate(-7.2,-0.2,"-7"),
locate(-6.2,-0.2,"-6"),
locate(-5.2,-0.2,"-5"),
locate(-4.2,-0.2,"-4"),
locate(-3.2,-0.2,"-3"),
locate(-2.2,-0.2,"-2"),
locate(-1.2,-0.2,"-1"),
locate(-0.2,-0.2,"0"),
locate(0.8,-0.2,"1"),
locate(1.8,-0.2,"2"),
locate(2.8,-0.2,"3"),
locate(3.8,-0.2,"4"),


blue(circle(-6,0,0.06)),
blue(circle(-6,0,0.08)),
blue(circle(-6,0,0.10)),
blue(circle(-6,0,0.12)),
blue(circle(-6,0,0.14)),
blue(circle(-6,0,0.16)),
blue(circle(-6,0,0.18)),
blue(circle(-6,0,0.20)),
blue(circle(-6,0,0.22)),
blue(locate(-6,1.2,"A")),

blue(circle(2,0,0.06)),
blue(circle(2,0,0.08)),
blue(circle(2,0,0.10)),
blue(circle(2,0,0.12)),
blue(circle(2,0,0.14)),
blue(circle(2,0,0.16)),
blue(circle(2,0,0.18)),
blue(circle(2,0,0.20)),
blue(circle(2,0,0.22)),
blue(locate(2,1.2,"B")),

blue(circle(-13,0,0.06)),
blue(circle(-13,0,0.08)),
blue(circle(-13,0,0.10)),
blue(circle(-13,0,0.12)),
blue(circle(-13,0,0.14)),
blue(circle(-13,0,0.16)),
blue(circle(-13,0,0.18)),
blue(circle(-13,0,0.20)),
blue(circle(-13,0,0.22)),
blue(locate(-13,1.2,"C")),

red(arc(-2,1.2,8+0.22,3,180,352)),
red(line(2,1.3,1.3,1.5)),
red(line(2,1.3,2.2,2.2)),

red(arc(-5.5,-1.2,15-0.22,3,0,180)),
red(line(-13+0.18,-1.3,-12.5+0.18,-1.5)),
red(line(-13+0.18,-1.3,-12.7+0.18,-2.2)),

red(locate(-4,4,matrix(1,4,"Move","8","units","right"))),
red(locate(-9,-3,matrix(1,4,"Move","15","units","left")))
)
}}}
Going from A to B shows that: -6+8 = 2
Going from B to C shows that: 2-15 = -13


Answer: <font color=red>-13</font>


============================================================================================


Method 2


Consider a smaller example of "3 left" then "2 right"
Draw 3 arrows pointing to the left.
Draw 2 arrows pointing to the right.
{{{
drawing(400,200,-16+5,5+5,-5+2,5+2,
line(1,2.2, 2.5,2.2),
line(2.5,2.2, 2.5,2.6),
line(2.5,2.6, 1,2.6),
line(1,2.6, 1,3.2),
line(1,3.2, -0.5,2.4),
line(-0.5,2.4, 1,1.6),
line(1,1.6, 1,2.2),

line(1+-3.2,2.2+0,2.5+-3.2,2.2+0),
line(2.5+-3.2,2.2+0,2.5+-3.2,2.6+0),
line(2.5+-3.2,2.6+0,1+-3.2,2.6+0),
line(1+-3.2,2.6+0,1+-3.2,3.2+0),
line(1+-3.2,3.2+0,-0.5+-3.2,2.4+0),
line(-0.5+-3.2,2.4+0,1+-3.2,1.6+0),
line(1+-3.2,1.6+0,1+-3.2,2.2+0),

line(1+-6.4,2.2+0,2.5+-6.4,2.2+0),
line(2.5+-6.4,2.2+0,2.5+-6.4,2.6+0),
line(2.5+-6.4,2.6+0,1+-6.4,2.6+0),
line(1+-6.4,2.6+0,1+-6.4,3.2+0),
line(1+-6.4,3.2+0,-0.5+-6.4,2.4+0),
line(-0.5+-6.4,2.4+0,1+-6.4,1.6+0),
line(1+-6.4,1.6+0,1+-6.4,2.2+0),

line(3.5+-7,2.2+-2,3.5+-7,2.6+-2),
line(3.5+-7,2.6+-2,5+-7,2.6+-2),
line(5+-7,2.6+-2,5+-7,3.2+-2),
line(5+-7,3.2+-2,6.5+-7,2.4+-2),
line(6.5+-7,2.4+-2,5+-7,1.6+-2),
line(5+-7,1.6+-2,5+-7,2.2+-2),
line(5+-7,2.2+-2,3.5+-7,2.2+-2),

line(3.5+-7.2+3.4,2.2+-2,3.5+-7.2+3.4,2.6+-2),
line(3.5+-7.2+3.4,2.6+-2,5+-7.2+3.4,2.6+-2),
line(5+-7.2+3.4,2.6+-2,5+-7.2+3.4,3.2+-2),
line(5+-7.2+3.4,3.2+-2,6.5+-7.2+3.4,2.4+-2),
line(6.5+-7.2+3.4,2.4+-2,5+-7.2+3.4,1.6+-2),
line(5+-7.2+3.4,1.6+-2,5+-7.2+3.4,2.2+-2),
line(5+-7.2+3.4,2.2+-2,3.5+-7.2+3.4,2.2+-2)
)
}}}


We have 2 of each type of arrow pair up and cancel out (since one direction undoes the other)

{{{
drawing(400,200,-16+5,5+5,-5+2,5+2,
red(line(-4,3.5,3,3.5)),
red(line(3,3.5,3,-1)),
red(line(3,-1,-4,-1)),
red(line(-4,-1,-4,3.5)),

red(line(-4,3.5,3,-1)),
red(line(-4,3.5+0.03,3,-1+0.03)),

red(line(3,3.5,-4,-1)),
red(line(3,3.5-0.03,-4,-1-0.03)),

line(1,2.2, 2.5,2.2),
line(2.5,2.2, 2.5,2.6),
line(2.5,2.6, 1,2.6),
line(1,2.6, 1,3.2),
line(1,3.2, -0.5,2.4),
line(-0.5,2.4, 1,1.6),
line(1,1.6, 1,2.2),

line(1+-3.2,2.2+0,2.5+-3.2,2.2+0),
line(2.5+-3.2,2.2+0,2.5+-3.2,2.6+0),
line(2.5+-3.2,2.6+0,1+-3.2,2.6+0),
line(1+-3.2,2.6+0,1+-3.2,3.2+0),
line(1+-3.2,3.2+0,-0.5+-3.2,2.4+0),
line(-0.5+-3.2,2.4+0,1+-3.2,1.6+0),
line(1+-3.2,1.6+0,1+-3.2,2.2+0),

line(1+-6.8,2.2+0,2.5+-6.8,2.2+0),
line(2.5+-6.8,2.2+0,2.5+-6.8,2.6+0),
line(2.5+-6.8,2.6+0,1+-6.8,2.6+0),
line(1+-6.8,2.6+0,1+-6.8,3.2+0),
line(1+-6.8,3.2+0,-0.5+-6.8,2.4+0),
line(-0.5+-6.8,2.4+0,1+-6.8,1.6+0),
line(1+-6.8,1.6+0,1+-6.8,2.2+0),

line(3.5+-7,2.2+-2,3.5+-7,2.6+-2),
line(3.5+-7,2.6+-2,5+-7,2.6+-2),
line(5+-7,2.6+-2,5+-7,3.2+-2),
line(5+-7,3.2+-2,6.5+-7,2.4+-2),
line(6.5+-7,2.4+-2,5+-7,1.6+-2),
line(5+-7,1.6+-2,5+-7,2.2+-2),
line(5+-7,2.2+-2,3.5+-7,2.2+-2),

line(3.5+-7.2+3.4,2.2+-2,3.5+-7.2+3.4,2.6+-2),
line(3.5+-7.2+3.4,2.6+-2,5+-7.2+3.4,2.6+-2),
line(5+-7.2+3.4,2.6+-2,5+-7.2+3.4,3.2+-2),
line(5+-7.2+3.4,3.2+-2,6.5+-7.2+3.4,2.4+-2),
line(6.5+-7.2+3.4,2.4+-2,5+-7.2+3.4,1.6+-2),
line(5+-7.2+3.4,1.6+-2,5+-7.2+3.4,2.2+-2),
line(5+-7.2+3.4,2.2+-2,3.5+-7.2+3.4,2.2+-2)
)
}}}
At the end of the day, the net change is "1 unit to the left"
This is one visual way to see how -3+2 = -1
And it's also a way to write 2+(-3) = -1



Use that example mentioned above to draw 8 arrows pointing to the right.
Then draw 15 arrows pointing to the left.


Circle 8 copies of each arrow type. Notice these arrows cancel each other out. 
The arrows pointing right will go away entirely. 


We'll have 7 arrows pointing to the left after the cancellation. This is because 15-8 = 7.


Therefore, the phrase "move right 8 units and then move left 15 units" can be shortened to "move 7 units to the left".


Draw a number line. Plot -6 on it. Then move 7 units to the left to arrive at -13.
This is the process of going from A to B as shown below.
{{{
drawing(600, 200, -16,5,-5,5,
line(-15-3,0,4+3,0),
line(-15,0.2,-15,-0.2),
line(-14,0.2,-14,-0.2),
line(-13,0.2,-13,-0.2),
line(-12,0.2,-12,-0.2),
line(-11,0.2,-11,-0.2),
line(-10,0.2,-10,-0.2),
line(-9,0.2,-9,-0.2),
line(-8,0.2,-8,-0.2),
line(-7,0.2,-7,-0.2),
line(-6,0.2,-6,-0.2),
line(-5,0.2,-5,-0.2),
line(-4,0.2,-4,-0.2),
line(-3,0.2,-3,-0.2),
line(-2,0.2,-2,-0.2),
line(-1,0.2,-1,-0.2),
line(0,0.2,0,-0.2),
line(1,0.2,1,-0.2),
line(2,0.2,2,-0.2),
line(3,0.2,3,-0.2),
line(4,0.2,4,-0.2),
locate(-15.5,-0.2,"-15"),
locate(-14.5,-0.2,"-14"),
locate(-13.5,-0.2,"-13"),
locate(-12.5,-0.2,"-12"),
locate(-11.5,-0.2,"-11"),
locate(-10.5,-0.2,"-10"),
locate(-9.2,-0.2,"-9"),
locate(-8.2,-0.2,"-8"),
locate(-7.2,-0.2,"-7"),
locate(-6.2,-0.2,"-6"),
locate(-5.2,-0.2,"-5"),
locate(-4.2,-0.2,"-4"),
locate(-3.2,-0.2,"-3"),
locate(-2.2,-0.2,"-2"),
locate(-1.2,-0.2,"-1"),
locate(-0.2,-0.2,"0"),
locate(0.8,-0.2,"1"),
locate(1.8,-0.2,"2"),
locate(2.8,-0.2,"3"),
locate(3.8,-0.2,"4"),

blue(circle(-6,0,0.06)),
blue(circle(-6,0,0.08)),
blue(circle(-6,0,0.10)),
blue(circle(-6,0,0.12)),
blue(circle(-6,0,0.14)),
blue(circle(-6,0,0.16)),
blue(circle(-6,0,0.18)),
blue(circle(-6,0,0.20)),
blue(circle(-6,0,0.22)),
blue(locate(-6,1.2,"A")),

blue(circle(-13,0,0.06)),
blue(circle(-13,0,0.08)),
blue(circle(-13,0,0.10)),
blue(circle(-13,0,0.12)),
blue(circle(-13,0,0.14)),
blue(circle(-13,0,0.16)),
blue(circle(-13,0,0.18)),
blue(circle(-13,0,0.20)),
blue(circle(-13,0,0.22)),
blue(locate(-13,1.2,"B")),

red(arc(-9.5,-1.2,7-0.22,3,0,180)),
red(line(-13+0.18,-1.3,-12.5+0.18,-1.5)),
red(line(-13+0.18,-1.3,-12.7+0.18,-2.2)),

red(locate(-11,-3,matrix(1,4,"Move","7","units","left")))
)
}}}


Answer: <font color=red>-13</font>
</font>