Answer
$z=18$
$r=3$
$s=3$
$p=3$
$a=3/4$
Work Step by Step
Two matrices are equal if they have the same dimension and
if corresponding elements, position by position, are equal.
---
Adding the two matrices on the LHS,
$\left[\begin{array}{lll}
-16+z & 12r & 8s+3\\
6p+2 & 7 & 9
\end{array}\right]=\left[\begin{array}{lll}
2 & 36 & 27\\
20 & 7 & 12a
\end{array}\right]$
The dimensions are both 2$\times$3, so we equate, position by position
$-16+z=2 \quad \Rightarrow \quad z=18$
$12r=36 \quad \Rightarrow \quad r=3$
$8s+3=27\quad \Rightarrow \quad 8s=24 \quad \Rightarrow \quad s=3$
$6p+2=20 \quad \Rightarrow \quad 6p=18\quad \Rightarrow \quad p=3$
$9=12a \quad \Rightarrow \quad a=3/4$
