Answer
$(-7,\infty)$
See the figure below.
Work Step by Step
Distribute $-2$ and then add $6$ to both sdies to obtain
$$
- 2(x + 3 )\lt 8 \Longrightarrow -2x-6 \lt 8\\
\Longrightarrow -2x-6 +6\lt 8+6 \Longrightarrow -2x\lt 14
.$$
Divide by $-2$ and reverse the inquality since we divide by a negative value, we get
$$
-2x\lt 14 \Longrightarrow x \gt -7
.$$
In terms of intervals, $x\in (-7,\infty)$.
To graph, plot a circle at $x=-7$ then shade the region to its right.
See the figure below.
