#### Answer

$(-7,1)$; see graph.

#### Work Step by Step

Step 1. From $3|2x+6|-9\lt 15$, we have $|2x+6|\lt 8$, which can be written as $-8\lt 2x+6 \lt 8$
Step 2. Solving the above inequality, we have $-14\lt 2x \lt 2$ and $-7\lt x \lt 1$, or in interval notation $(-7,1)$.
Step 3. We can graph the above solution on a number line as shown.