You can put this solution on YOUR website! First simplify to isolate the absolute value expression on the LHS:
-2|x+1| = -8
|x+1| = 4
This gives two solutions:
x+1 = 4
x = 3
and
-(x+1) = 4
x+1 = -4
x = -5
Check:
-2(3+1) + 4 = -4
-4 = -4
-2*|-4| + 4 = -4