#### Answer

$-16\le x \le 8$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
\left| \dfrac{x+4}{6} \right|\le2
,$ use the definition of a less than (less than or equal to) absolute value inequality. Then use the properties of inequality to isolate the variable.
$\bf{\text{Solution Details:}}$
Since for any $c\gt0$, $|x|\lt c$ implies $-c\lt x\lt c$ (or $|x|\le c$ implies $-c\le x\le c$), the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2\le \dfrac{x+4}{6} \le2
.\end{array}
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-2\le \dfrac{x+4}{6} \le2
\\\\
6\cdot(-2)\le 6\cdot\dfrac{x+4}{6} \le6\cdot2
\\\\
-12\le x+4 \le 12
\\\\
-12-4\le x+4-4 \le 12-4
\\\\
-16\le x \le 8
.\end{array}
Hence, the solution set $
-16\le x \le 8
.$