It is given that $X=\left[ \begin{matrix}
p & q \\
8 & 5 \\
\end{matrix} \right],Y=\left[ \begin{matrix}
3p & 5q \\
2q & 7 \\
\end{matrix} \right]$
Now we have to add $2$ given matrices
$X+Y=\left[ \begin{matrix}
p+3p & q+5q \\
8+2q & 5+7 \\
\end{matrix} \right]$
So, $X+Y=\left[ \begin{matrix}
4p & 6q \\
8+2q & 12 \\
\end{matrix} \right]$….(1)
But it is given that, $X+Y=\left[ \begin{matrix}
12 & 6 \\
2r & 3s \\
\end{matrix} \right]$…..(2)
From (1) and (2) we get,
$\left[ \begin{matrix}
4p & 6q \\
8+2q & 12 \\
\end{matrix} \right]=\left[ \begin{matrix}
12 & 6 \\
2r & 3s \\
\end{matrix} \right]$
Then,
$4p=12$
$p=12/4$
$p=3$
$6q=6$
$q=6/6$
$q=1$
$8+2q=2r$
$8+2(1)=2r$
$8+2=2r$
$r=10/2$
$r=5$
$12=3s$
$s=12/3$
$s=4$