Question 729979
The variable expression, x+4, may be either positive or negative, depending on the value of x.  


When {{{x+4>=0}}}, {{{y=2abs(x+4)}}} is {{{y=2(x+4)}}} or {{{y=2x+8}}}.  You must restrict the graph of this line to satisfy {{{x+4>0}}} which is {{{x>=-4}}}.  


When {{{x+4<0}}}, {{{y=2abs(x+4)}}} is {{{y=2*(-1)(x+4)}}}, or {{{y=2(-x-4)}}}, or {{{y=-2x-8}}}.  You must restrict the graph of this line to satisfy {{{x+4<0}}} which is {{{x<-4}}}.  


IN CASE OF CONTINUED DIFFICULTY:
The absolute value of an expression requires simple but careful attention to logic.  |x+4| will always be positive or zero.  NEVER Negative.  
If x+4=0>0, then |x+4|=x+4.  
If x+4<0, then |x+4|=-(x+4)=-x-4.  
Really that is based on the meaning of absolute value.  
For any variable, v, we can consider how far is v from zero on the number line.  |v| is the distance from zero on the number line.  v is a variable, so by itself, we do not know its value; but |v| is equal to v if {{{v>=0}}}, and |v| is equal to -v if {{{v<0}}}.  
Drawing a number line makes this easier to SEE.