Answer
$y=-4\text{ OR }y=8$
Work Step by Step
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation, $
|2y-4|=12
,$ implies
\begin{array}{l}\require{cancel}
2y-4=12
\\\\\text{OR}\\\\
2y-4=-12
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2y-4=12
\\
2y-4+4=12+4
\\
2y=16
\\
\dfrac{2y}{2}=\dfrac{16}{2}
\\
y=8
\\\\\text{OR}\\\\
2y-4=-12
\\
2y-4+4=-12+4
\\
2y=-8
\\
\dfrac{2y}{2}=-\dfrac{8}{2}
\\
y=-4
.\end{array}
Hence, $
y=-4\text{ OR }y=8
.$
