In how many ways can you place 4 indistinguishable rooks on a chess board so that no two rooks attack each other and there is one rook in each quadrant shown below? (A rook attacks every square in its row and column.) 8x8 Board

There are 1904 ways.

It is 20736 since 16x12x12x9

for 1st 2nd and 3rd rook