Answer
92, Yes.
Work Step by Step
Evaluate the determinant with row4 cofactors: (use row4 or row 3 instead of row1 as they contains two zeros)
$\begin{array}( \\|A|= \\ \\ \end{array}
\begin{vmatrix} 1 & 2 &0&2\\3 &-4 &0&4\\0 &1 &6&0\\1 &0 &2&0 \end{vmatrix} \begin{array}( \\=(-1) \\ \\\end{array}\begin{vmatrix} 2 &0&2\\-4 &0&4\\1 &6&0 \end{vmatrix} \begin{array}( \\(-2) \\ \\\end{array}\begin{vmatrix} 1 &2&2\\3 &-4&4\\0 &1&0 \end{vmatrix}$
$|A|=(-1)(2(-24)+2(-24))-2((-1)(4-6))=96-4=92$
(here evaluate the 3x3 the best way you can.)
As $|A|\ne0$, the matrix should have an inverse.
