#### Answer

$x=\{ -12,12 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of absolute value equality to solve the given equation, $
|x|=12
.$ Do checking of the solution/s.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|=c$ implies $x=c \text{ or } x=-c,$ the equation above is equivalent to
\begin{array}{l}\require{cancel}
x=12
\\\\\text{OR}\\\\
x=-12
.\end{array}
If $x=12,$ then
\begin{array}{l}\require{cancel}
|12|=12
\\\\
12=12
\text{ (TRUE)}
.\end{array}
If $x=-12,$ then
\begin{array}{l}\require{cancel}
|-12|=12
\\\\
12=12
\text{ (TRUE)}
.\end{array}
Hence, $
x=\{ -12,12 \}
.$