Hi
XA + XB = C
X(A+B) = C
X(A+B)(A+B)-1 = C(A+B)-1
X = C(A+B)-1
$$A+B= \begin{pmatrix}4 &2 \\1 &4 \end{pmatrix} \\(A+B)^{-1} = \begin{pmatrix}\frac{2}{7} &-\frac{1}{7} \\-\frac{1}{14} &\frac{2}{7} \end{pmatrix} \\X = C(A+B)^{-1} = \begin{pmatrix}-6 &32 \\-3 &2 \end{pmatrix} \begin{pmatrix}\frac{2}{7} &-\frac{1}{7} \\-\frac{1}{14} &\frac{2}{7} \end{pmatrix} = \begin{pmatrix}-4 &10 \\-1 &1 \end{pmatrix}$$
Probe
$$ X(A+B) = \begin{pmatrix}-4 &10 \\-1 &1 \end{pmatrix} \begin{pmatrix}4 &2 \\1 &4 \end{pmatrix} = \begin{pmatrix}-6 &32 \\-3 &2 \end{pmatrix} = C \\\Rightarrow BINGO \ :-) $$