#### Answer

$y=\left\{ -9,9 \right\}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given equation, $
|2y|-5=13
,$ isolate first the absolute value expression. Then use the definition of an absolute value equality.
$\bf{\text{Solution Details:}}$
Using the properties of equality, the given equation is equivalent to
\begin{array}{l}\require{cancel}
|2y|-5=13
\\\\
|2y|=13+5
\\\\
|2y|=18
.\end{array}
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the given equation is equivalent to
\begin{array}{l}\require{cancel}
2y=18
\\\\\text{OR}\\\\
2y=-18
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
2y=18
\\\\
y=\dfrac{18}{2}
\\\\
y=9
\\\\\text{OR}\\\\
2y=-18
\\\\
y=-\dfrac{18}{2}
\\\\
y=-9
.\end{array}
Hence, $
y=\left\{ -9,9 \right\}
.$