Answer
$x=\left\{ -14,26 \right\}$
Work Step by Step
Since $|x|=a$ implies $x=a \text{ OR } x=-a$, then the statement $
\left|\dfrac{6-x}{4} \right|=5
$ evaluates to
\begin{array}{l}
\dfrac{6-x}{4}=5\\\\
6-x=20\\
-x=14\\
x=-14
,\\\\\text{OR}\\\\
\dfrac{6-x}{4}=-5\\\\
6-x=-20\\
-x=-26\\
x=26
.\end{array}
Hence, the solution set is $
x=\left\{ -14,26 \right\}
$.