Expansion along a row

Expansion along the second row. The only nonzero entry is $a_{22}=3$. Its cofactor is $(-1)^{2+2}=+1$ times the determinant of the $3\times3$ minor obtained by deleting row $2$ and column $2$:
$$M_{22} = \begin{vmatrix} 2 & 0 & 1 \\ 0 & 4 & 0 \\ 5 & 0 & 6 \end{vmatrix}.$$

Expand $M_{22}$ along its second row. The only nonzero entry is $4$ at position $(2,2)$, cofactor $(+1)\begin{vmatrix}2&1\\5&6\end{vmatrix} = 12-5=7$.

So $M_{22} = 4\cdot7 = 28$.

Conclusion. $\det A = 3\cdot28 = 84$.

Check by permutation formula. The matrix is a block "diagonal with a corner" structure; the result $2\cdot3\cdot4\cdot6 + (\text{sign})\cdot1\cdot3\cdot4\cdot5 = 144 - 60 = 84$ confirms it.