Answer
$$\lim _{x \rightarrow 2} \frac{3 x-6}{x+2} =0$$
Work Step by Step
Given $$\lim _{x \rightarrow 2} \frac{3 x-6}{x+2}$$
using the method of replacement
\begin{align*}
\lim _{x \rightarrow 2} \frac{3 x-6}{x+2}&=\lim _{x \rightarrow 2} \frac{3 (2)-6}{2+2}\\
&=\lim _{x \rightarrow 2} \frac{0}{4}\\
&=0
\end{align*}