Answer
$\left( -\infty,-7 \right)\cup(9,\infty)$
Work Step by Step
Using the properties of inequality, the given expression, $
|-1+x|-6\gt2
,$ is equivalent to
\begin{array}{l}\require{cancel}
|-1+x|\gt2+6
\\\\
|-1+x|\gt8
.\end{array}
Since for any $a\gt0$, $|x|\gt a$ implies $x\gt a$ OR $x\lt -a$, then the inequality, $
|-1+x|\gt8
,$ is equivalent to
\begin{array}{l}\require{cancel}
-1+x\gt8
\\\\
x\gt8+1
\\\\
x\gt9
,\\\\\text{OR}\\\\
-1+x\lt-8
\\\\
x\lt-8+1
\\\\
x\lt-7
.\end{array}
Hence, the solution set is $
\left( -\infty,-7 \right)\cup(9,\infty)
.$
See graph below.