Answer
The vertical asymptote is the line $x=0$.
The horizontal asymptote is the line $y=6$.

Work Step by Step
Given: $\frac{-3}{x}+6$
$x=0$
The vertical asymptote is the line $x=0$.
The horizontal asymptote is the line $y=6$.
Make a list of values:
$x=-1 \rightarrow y=9$
$x=-3 \rightarrow y=7$
$x=0 \rightarrow y=6$
$x=1\rightarrow y=3$
$x=3\rightarrow y=5$