$\text{Let }|A|=\begin{vmatrix}2 &0 &0 &0 \\ 8& 1& 7& 2\\ 2& 0&2 &0 \\ 9&0 & 6 & 1 \end{vmatrix}$
$\implies |A|=2\times\begin{vmatrix} 1& 7& 2\\ 0&2 &0 \\ 0 & 6 & 1 \end{vmatrix}$
$\implies |A|=2\times 1\times \begin{vmatrix} 2 &0 \\ 6 & 1 \end{vmatrix}$
$\implies |A|=2\times 1\times (2-0)$
$\implies |A|=2\times 1\times 2=4$
Answer$: A$