Answer
$$D_f=(-6, \infty )$$
Work Step by Step
Please note that the function $\log_bM$ is defined if and only if $M \gt 0$. So for the function $f(x)=\log_3(x+6)$ we have$$x+6 \gt 0 \quad \Rightarrow \quad x \gt -6.$$Thus, the domain of the function is$$D_f=(-6, \infty ).$$
