Answer
$$\begin{pmatrix}-\frac{5}{36}&-\frac{11}{72}\\ -\frac{1}{12}&-\frac{1}{24}\end{pmatrix}$$
Work Step by Step
We know the following equation for the inverse of a matrix:
$$\begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}^{-1}=\frac{1}{\det \begin{pmatrix}a\:&\:b\:\\ c\:&\:d\:\end{pmatrix}}\begin{pmatrix}d\:&\:-b\:\\ -c\:&\:a\:\end{pmatrix}$$
Thus:
$$ \frac{1}{\det \begin{pmatrix}6&-22\\ -12&20\end{pmatrix}}\begin{pmatrix}20&-\left(-22\right)\\ -\left(-12\right)&6\end{pmatrix} \\ \begin{pmatrix}-\frac{5}{36}&-\frac{11}{72}\\ -\frac{1}{12}&-\frac{1}{24}\end{pmatrix}$$
