Answer
$$\lim\limits_{t \to 3}g(t)=4.$$
Work Step by Step
Since $\lim\limits_{t \to 3}tg(t)$ exists, then we can apply the product law as follows
$$\lim\limits_{t \to 3}tg(t)=12\Longrightarrow \lim\limits_{t \to 3}t\lim\limits_{t \to 3}g(t)=12.$$
But, $\lim\limits_{t \to 3}t=3$, so we have
$$3\lim\limits_{t \to 3}g(t)=12\Longrightarrow \lim\limits_{t \to 3}g(t)=4.$$
