#### Answer

$\left[ -3,3 \right]$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-6 \le \dfrac{4}{3}x-2 \le 2
,$ use the properties of inequality to isolate the variable.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality to isolate the variable results to
\begin{array}{l}\require{cancel}
3(-6) \le 3\left( \dfrac{4}{3}x-2 \right) \le 3(2)
\\\\
-18 \le 4x-6 \le 6
\\\\
-18+6 \le 4x-6+6 \le 6+6
\\\\
-12 \le 4x \le 12
\\\\
\dfrac{-12}{4} \le \dfrac{4x}{4} \le \dfrac{12}{4}
\\\\
-3 \le x \le 3
.\end{array}
In interval notation, the solution set is $
\left[ -3,3 \right]
.$
The colored graph is the graph of the solution set.