Answer
$A=(1/256)*\left[\begin{array}{cc}
8&-16\\
12&8
\end{array} \right]$
Work Step by Step
Given $(4A)^{-1}=\left[\begin{array}{cc}
2&4\\
-3&2
\end{array} \right]$
thus $ (1/4)A^{-1}=\left[\begin{array}{cc}
2&4\\
-3&2
\end{array} \right]$
$A^{-1}=\left[\begin{array}{cc}
8&16\\
-12&8
\end{array} \right]$
Since $A=(A^{-1})^{-1}=(1/|A^{-1}|)*\left[\begin{array}{cc}
8&-16\\
12&8
\end{array} \right]=(1/256)*\left[\begin{array}{cc}
8&-16\\
12&8
\end{array} \right]$