Answer
$\begin{bmatrix}
50 & -3\\
18 & 21
\end{bmatrix}$
Work Step by Step
Since, $A+B$ is a $2 \times 3$ matrix and $C$ is a $3 \times 2$ matrix, we know that $(A+B)C$ is defined and results in a $2 \times 2$ matrix.
$A+B=\begin{bmatrix}
0+4 & 3+1 & -5+0\\
1+(-2) & 2+3 & 6+(-2)
\end{bmatrix}\\=\begin{bmatrix}
4 & 4 & -5 \\
1-2 & 5 & 6-2
\end{bmatrix}\\=\begin{bmatrix}
4 & 4 & -5\\
-1 & 5 & 4
\end{bmatrix}$
Now, $(A+B)C=\left[\begin{array}{lll}
4 & 4 & -5\\
-1 & 5 & 4
\end{array}\right]\left[\begin{array}{ll}
4 & 1\\
6 & 2\\
-2 & 3
\end{array}\right] \\=\left[\begin{array}{ll}
16+24+10 & 4+8-15\\
-4+30-8 & -1+10+12
\end{array}\right] \\=\begin{bmatrix}
50 & -3\\
18 & 21
\end{bmatrix}$
