Answer
$y\le-9 \text{ OR } y\ge15$
Work Step by Step
Since for any $c\gt0$, $|x|\gt c$ implies $x\gt c \text{ or } x\lt-c$ (which is equivalent to $|x|\ge c$ implies $x\ge c \text{ or } x\le-c$), the given inequality, $
|y-3|\ge12
,$ implies
\begin{array}{l}\require{cancel}
y-3\ge12
\\\\\text{OR}\\\\
y-3\le-12
.\end{array}
Solving each inequality results to
\begin{array}{l}\require{cancel}
y-3\ge12
\\
y-3+3\ge12+3
\\
y\ge15
\\\\\text{OR}\\\\
y-3\le-12
\\
y-3+3\le-12+3
\\
y\le-9
.\end{array}
Hence, the solution is $
y\le-9 \text{ OR } y\ge15
$.
The graph of the solution above is shown below.
