Answer
$-4 \le x \le 2$
Refer to the graph below.
Work Step by Step
Solve each inequality:
\begin{align*}
3x &\ge -12\\\\
\frac{3x}{3} &\ge \frac{-12}{3}\\\\
x &\ge -4
\end{align*}
$$\text{and}$$
\begin{align*}
8x&\le 16\\\\
\frac{8x}{8} &\le \frac{16}{8}\\\\
x&\le 2
\end{align*}
Graph each inequality to obtain the one in the attached image below.
Since the compound inequality involves the conjunction $\text{AND}$, then the solutions to the inequality are numbers common to both graphs, which are the numbers in the interval $-4 \le x \le 2$.
