Answer
$x=-4 \text{ or } x =4$
Work Step by Step
Subtract 8 to both sides to have:
$\\8+|4c|-8 = 24-8
\\|4c|=16$
RECALL:
$\\|a| = a \text{ if} a \ge 0
\\|a| = -a \text{ if } a \lt 0$
Use this definition to have:
$\\4c = 16 \text{ or } 4c = -16
\\c=4 \text{ or } c = -4$
