Answer
Horizontal asymptote:$\qquad y=-2$
(graphed at desmos.com)
Work Step by Step
$\displaystyle \lim_{x\rightarrow\infty}(\frac{3}{x}-2)=-2$
$\displaystyle \lim_{x\rightarrow-\infty}(\frac{3}{x}-2)=-2$
Horizontal asymptote:$\qquad y=-2$