Answer
$\left( -\infty,-1 \right)\cup(1,\infty)$
Work Step by Step
Since for any $a\gt0$, $|x|\gt a$ implies $x\gt a$ OR $x\lt -a$, then the given inequality, $
|y|\gt1
,$ is equivalent to
\begin{array}{l}\require{cancel}
y\gt1
,\\\\\text{OR}\\\\
y\lt-1
.\end{array}
Hence, the solution set is $
\left( -\infty,-1 \right)\cup(1,\infty)
.$
See graph below.