Question 116169
The absolute value function has two values and you have to solve for both. 
When (x+6)>0, then
{{{abs(x+6)=x+6}}}
{{{x+6=2x}}}
{{{x=6}}}
When (x+6)<0, then
{{{abs(x+6)=-(x+6)}}}
{{{-(x+6)=2x}}}
{{{-x-6=2x}}}
{{{3x=-6}}}
{{{x=-2}}}
Check your answers.
{{{abs(x+6)=2x}}}
{{{abs(6+6)=2*6}}}
{{{12=12}}}
True statement. 
Good answer.
{{{abs(x+6)=2x}}}
{{{abs(-2+6)=2*(-2)}}}
{{{abs(4)=-4}}}
{{{4=-4}}}
False statement. 
Not a good answer. 
Here's why.
When we looked at the second solution, 
we said "When (x+6)<0"
{{{(x+6)<0}}}
{{{x<-6}}}
We got an answer x=-2 which is not less than -6, so the answer is not valid. 
There is only one solution. 
x=6.