Answer
$$ t=\pm \sqrt{ \pi+4} $$
Work Step by Step
Since $$\sin y+y=t^{2}+C$$
is a solution and $y(2)=0$, then
$$\sin (0) +0 =4+C\ \ \Rightarrow C=-4 $$
Hence the particular solution is
$$\sin y+y=t^{2}+4$$
We find the $t$ that satisfies $ y( t)=\pi $,
\begin{align*}
\sin \pi+\pi&=t^{2}-4\\
\pi+4&=t^2
\end{align*}
Then $$ t=\pm \sqrt{ \pi+4}$$
