Answer
-4/3, 4
Work Step by Step
Since this is an absolute value expression, the value inside the absolute value can be positive or negative. Thus, considering both possibilities:
$$ 4-3x =8 \\ -3x =4 \\ x=-\frac{4}{3} \\ OR \\ 4-3x = -8 \\ -3x =-12 \\ x=4$$