#### Answer

$b=\{ 4,20 \}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Use the definition of absolute value equality to solve the given equation, $
|b-12|=8
.$ 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}
b-12=8
\\\\\text{OR}\\\\
b-12=-8
.\end{array}
Solving each equation results to
\begin{array}{l}\require{cancel}
b-12=8
\\\\
b=8+12
\\\\
b=20
\\\\\text{OR}\\\\
b-12=-8
\\\\
b=-8+12
\\\\
b=4
.\end{array}
If $b=20,$ then
\begin{array}{l}\require{cancel}
|b-12|=8?
\\\\
|20-12|=8?
\\\\
|8|=8?
\\\\
8=8
\text{ (TRUE)}
.\end{array}
If $b=4,$ then
\begin{array}{l}\require{cancel}
|b-12|=8?
\\\\
|4-12|=8?
\\\\
|-8|=8?
\\\\
8=8
\text{ (TRUE)}
.\end{array}
Hence, $
b=\{ 4,20 \}
.$