Answer A)
Rooks only can go in straight line
So, 1 st rook can arrange any of $8^{2}$ ways
2nd rook can arrange in $7^{2}$
Similarly other rooks too.
Now, black rook and white rook are identical by themselves
So, black can arrange in $\frac{8^{2}.7^{2}}{2!}$
Similarly white can arrange in $\frac{6^{2}.5^{2}.4^{2}.3^{2}}{4!}$
So black and white can arrange in $\frac{\left ( 8.7\right )^{2}\left ( 6.5.4.3 \right )^{2}}{2!.4!}$