Not sure what you mean by "using diagonals", but I'll take a guess and say it refers to the trick where you copy the matrix like this,
[tex]\begin{vmatrix}-1&2&2\\4&-1&1\\3&2&2\end{vmatrix}\begin{matrix}-1&2&2\\4&-1&1\\3&2&2\end{matrix}[/tex]
Then the determinant is computed by taking the leftmost three left-to-right diagonals, multiplying elements on the same diagonal together, then adding the three products together:
[tex](-1)(-1)(2)+(2)(1)(3)+(2)(4)(2)=24[/tex]
Next, take the rightmost right-to-left diagonals, doing the same as before:
[tex](2)(-1)(3)+(2)(4)(2)+(-1)(1)(2)=8[/tex]
The determinant is then the difference of these two, so the answer would be 16 (A).
