#### Answer

$(-7,-6)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To solve the given inequality, $
-15 \lt 3x+6 \lt -12
,$ use the properties of inequality.
For the interval notation, use a parenthesis for the symbols $\lt$ or $\gt.$ Use a bracket for the symbols $\le$ or $\ge.$
For graphing inequalities, use a hollowed dot for the symbols $\lt$ or $\gt.$ Use a solid dot for the symbols $\le$ or $\ge.$
$\bf{\text{Solution Details:}}$
Using the properties of inequality, the inequality above is equivalent to
\begin{array}{l}\require{cancel}
-15-6 \lt 3x+6-6 \lt -12-6
\\\\
-21 \lt 3x \lt -18
\\\\
-\dfrac{21}{3} \lt \dfrac{3x}{3} \lt -\dfrac{18}{3}
\\\\
-7 \lt x \lt -6
.\end{array}
In interval notation, the solution set is $
(-7,-6)
.$
The red graph is the graph of the solution set.