Answer
$$\lim_{x \to 2^- }g(x)=0$$
Work Step by Step
Please note that the graph of $g(x)$ is the graph of $f(x)$ shifted two units to the left.
To find $\lim_{x\to 2^- }g(x)$, examine the graph of $g$ near $x=2$. As $x$ gets closer to $2$ from the left, the values of $g(x)$ get closer to $0$. We conclude from the graph that$$\lim_{x \to 2^- }g(x)=0.$$
