Answer
$(-\infty,-6)$ and $(0,\infty)$ , see figure.
Work Step by Step
Step 1. Given $|\frac{2x+6}{3}|\gt2$, we can rewrite the inequality as $\frac{2x+6}{3}\gt 2$ or
$\frac{2x+6}{3}\lt-2$
Step 2. Solve the first inequality as $2x+6\gt 6$ which gives $x\gt0$
Step 3. Solve the second inequality as $2x+6\lt-6$ which gives $x\lt-6$
Step 4. The above result can be represented in the interval form as $(-\infty,-6)$ and $(0,\infty)$
Step 5. Show the above intervals on a number line as in the figure.
