Answer
$\left( -\infty,4 \right)\cup(6,\infty)$
Work Step by Step
Since for any $a\gt0$, $|x|\gt a$ implies $x\gt a$ OR $x\lt -a$, then the given inequality, $
|0.6x-3|\gt0.6
,$ is equivalent to
\begin{array}{l}\require{cancel}
0.6x-3\gt0.6
\\\\
0.6x\gt0.6+3
\\\\
0.6x\gt3.6
\\\\
x\gt\dfrac{3.6}{0.6}
\\\\
x\gt6
,\\\\\text{OR}\\\\
0.6x-3\lt-0.6
\\\\
0.6x\lt-0.6+3
\\\\
0.6x\lt2.4
\\\\
x\lt\dfrac{2.4}{0.6}
\\\\
x\lt4
.\end{array}
Hence, the solution set is $
\left( -\infty,4 \right)\cup(6,\infty)
.$
See graph below.