Answer
$(0,\frac{14}{3}]$
Work Step by Step
$-6 \lt 3(x-2) \leq 8$
Using the properties of inequalities, divide all parts by 3
$\frac{-6}{3} \lt \frac{3(x-2)}{3} \leq \frac{8}{3}$
$-2 \lt x-2 \leq \frac{8}{3}$
Add 2 to all parts,
$-2+2 \lt x-2 +2 \leq \frac{8}{3}+2$
$0 \lt x \leq \frac{8}{3}+2$
Take LCD
$0 \lt x \leq \frac{8+6}{3}$
$0 \lt x \leq \frac{14}{3}$
In Interval Notation: $(0,\frac{14}{3}]$