Answer
$(-6,\infty)$
Work Step by Step
We are given the function:
$$f(x)=\log_3 (x+6).$$
The logarithmic function is defined when its argument is strictly positive, therefore we have:
$$\begin{align*}
x+6&>0\\
x&>-6.
\end{align*}$$
So the domain of the function $f$ is:
$$(-6,\infty).$$
