Answer
$(-6,0)$.
The graph is shown below.
Work Step by Step
The given expression is
$\Rightarrow \left | \frac{2x+6}{3}\right |\lt2$
Rewrite the inequality without absolute value bars.
$\Rightarrow -2\lt \frac{2x+6}{3}\lt2$
Solve compound inequality.
Multiply all three parts by $3$.
$\Rightarrow -2(3)\lt \frac{2x+6}{3}(3)\lt2(3)$
Simplify.
$\Rightarrow -6\lt 2x+6\lt6$
Add $-6$ to all three parts.
$\Rightarrow -6-6\lt 2x+6-6\lt6-6$
Simplify.
$\Rightarrow -12\lt 2x\lt0$
Divide by $2$ to all three parts.
$\Rightarrow \frac{-12}{2}\lt \frac{2x}{2}\lt\frac{0}{2}$
Simplify.
$\Rightarrow -6\lt x\lt0$
The solution set $(-6,0)$.
