Answer
$(a)\quad t=k\pi$
$(b) \quad 0$ and $\pi.$
Work Step by Step
The first task is to isolate the trigonometric function on one side:
Add $(-4)$ to both sides...
$3\sin t=4-4\qquad $ ... simplify
$ 3\sin t=0\quad$ ... divide with $3$
$\sin t=0$
Now, we find a reference angle. From the table of characteristic angles, we know that $\sin 0=0.$
Next, we know that within the interval $0\leq t \lt 2\pi $
the radian angles that satisfy the equation are $0$ and $\pi.$
Finally, to each individual solution, add multiples of $ 2\pi$ to cover all solutions:
$(a)$
$ t=0+2k\pi$ or $ t=\pi+2k\pi$
which can be combined and written as
$ t=k\pi$
$(b)$
The solutions within the interval $0\leq t \lt 2\pi:$
$0$ and $\pi.$