Question 137580
Let x=the larger number
and y=the smaller number

Now we are told that:

x+y=2(x-y) or
x+y=2x-2y subtract x and also y from each side
0=2x-x-2y-y  collect like terms
 x-3y=0---------------------------------------------eq1

We are also told that:
x=2y+6  subtract 2y from each side

x-2y=2y-2y+6
x-2y=6---------------------------------------------eq2
From eq1, we see that x=3y.  Substitute this into eq2
3y-2y=6
y=6---------------------------------------smaller number
substitute y=6 into eq1

x-18=0  add 18 to each side

x=18-------------------------------------larger number

CK
The sum of two numbers is twice their difference:
6+18=2*(18-6)
24=2*12
24=24
The larger number is 6 more than twice the smaller.
18=2*6+6
18=12+6
18=18


Hope this helps---ptaylor