The Six Pawns

In how many different ways may I place six pawns on the chessboard so that there shall be an even number of unoccupied squares in every row and every column? We are not here considering the diagonals at all, and every different six squares occupied makes a different solution, so we have not to exclude reversals or reflections.

Its source prints no answer for this problem, so there's nothing to check against.

H. E. Dudeney, Amusements in Mathematics (1917) · No. 358