Answer
Discontinuous at $ x=2$
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
$\lim_\limits{x \to 2^{-}} f(x)= \lim_\limits{x \to 2^{-}}3x=6$
and $\lim_\limits{x \to 2^{+}} f(x)= \lim_\limits{x \to 2^{+}}(x+4)=6$
So, $\lim_\limits{x \to 2^{-}} f(x)= \lim_\limits{x \to 2^{+}}f(x)$ exists.
Now, $\lim_\limits{x \to 2} f(x)=6$
and $ f(2)=5$
so, $\lim_\limits{x \to 2} f(x) \neq f(2)$
Therefore, the function is discontinuous at $ x=2$
