Answer
For the left-hand limit, we will be on the fourth piece which approaches $28$ as $t$ approaches $4$ and for the right-hand limit we will be on the fifth piece which approaches $56$ as $t$ approaches $4$.
That is,
$\lim_\limits{t \to 4^-}f(t)=28$
$\lim_\limits{t \to 4^+}f(t)=56$
Work Step by Step
Since, we are reducing the change in the $t$ from a different direction.
We will be on different pieces of the graph in both the limits.
Hence, for the left-hand limit, we will be on the fourth piece which approaches $28$ as $t$ approaches $4$ and for the right-hand limit we will be on the fifth piece which approaches $56$ as $t$ approaches $4$.
That is,
$\lim_\limits{t \to 4^-}f(t)=28$
$\lim_\limits{t \to 4^+}f(t)=56$
