2x2 matrix's inverse:
[tex]\begin{gathered} A^{(-1)}=\begin{bmatrix}{a} & {b} & {} \\ {c} & {d} & {}\end{bmatrix}^{(-1)}=\frac{1}{ad-bc}\begin{bmatrix}{d} & {-b} & {} \\ {-c} & {a} & \end{bmatrix} \\ \\ \\ It\text{ exists only if: } \\ ad-bc\ne0 \end{gathered}[/tex]For the given matrix:
[tex]\begin{gathered} \begin{bmatrix}{6} & {-3} & \\ {-8} & {4} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{6\times4-(-3)\times(-8)}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{24-24}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ A^{(-1)}=\frac{1}{0}\begin{bmatrix}{4} & {3} & {} \\ {8} & {6} & {}\end{bmatrix} \\ \\ \end{gathered}[/tex]As the determinat (ad-bc) is 0 the matrix isn't a invertible matrix. The inverse of the given matrix doesn't exist