Answer
$-\frac{4}{3}\text{ or }0$
Work Step by Step
$6\left| 3x+2 \right|=12$
Divide by $6$ on both sides,
$\begin{align}
& 6\left| 3x+2 \right|=12 \\
& \frac{6\left| 3x+2 \right|}{6}=\frac{12}{6} \\
& \left| 3x+2 \right|=2
\end{align}$
Therefore, $3x+2=-2$ or $3x+2=2$
For the equation $3x+2=-2$,
Subtract $\left( 2 \right)$ on both sides.
$\begin{align}
& 3x+2=-2 \\
& 3x+2-2=-2-2 \\
& 3x=-4
\end{align}$
Divide by $\left( 3 \right)$ on both sides,
$\begin{align}
& 3x=-4 \\
& \frac{3x}{3}=\frac{-4}{3} \\
& x=-\frac{4}{3}
\end{align}$
For the equation $3x+2=2$,
Subtract $\left( 2 \right)$ on both sides,
$\begin{align}
& 3x+2=2 \\
& 3x+2-2=2-2 \\
& 3x=0
\end{align}$
Divide by $\left( 3 \right)$ on both sides,
$\begin{align}
& 3x=0 \\
& \frac{3x}{3}=\frac{0}{3} \\
& x=0
\end{align}$
Thus, the required value of x is $-\frac{4}{3},0$.
