6. To color 8 small squares on a $4 \times 4$ chessboard black, such that each row and each column has exactly 2 black squares, there are $\qquad$ different coloring methods.
6. 90 The first row is colored with 2 black cells, there are $C_{4}^{2}$ ways to color;

After coloring the first row, the following three cases are discussed:
(1) The 2 black cells in the second row are in the same columns as the black cells in the first row, in this case, the coloring methods for the remaining rows are uniquely determined;
(2) The 2 black cells in the second row are in different columns from the black cells in the first row, in this case, there are $C_{4}^{2}$ ways to color the third row, and the coloring method for the fourth row is uniquely determined;
(3) The 2 black cells in the second row have exactly 1 in the same column as the black cells in the first row, there are $2 \times 2=4$ ways to color. After the first and second rows are colored, the black cell in the third row must be in a different column from the previously colored black cells, in this case, there are two ways to color the third row, and the coloring method for the fourth row is uniquely determined.
Therefore, there are $C_{4}^{2}\left(1+C_{4}^{2}+4 \times 2\right)=90$ ways to color.