Answer
$x=\left\{ -12,12 \right\}$
Work Step by Step
Since for any $a\gt0$, $|x|=a$ implies $x=a$ OR $x=-a$, then the given equation, $
|0.5x|=6
,$ is equivalent to
\begin{array}{l}\require{cancel}
0.5x=6 \text{ OR } 0.5x=-6
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
0.5x=6
\\\\
10(0.5x)=(6)10
\\\\
5x=60
\\\\
x=\dfrac{60}{5}
\\\\
x=12
\\\\\text{ OR }\\\\
0.5x=-6
\\\\
10(0.5x)=(-6)10
\\\\
5x=-60
\\\\
x=-\dfrac{60}{5}
\\\\
x=-12
.\end{array}
Hence, the solutions are $
x=\left\{ -12,12 \right\}
.$
