6. Fill in all the numbers $1,2, \cdots, 9$ into the $3 \times 3$ grid on the right, with one number in each cell, so that the numbers in each row increase from left to right, and the numbers in each column decrease from top to bottom. The number of different ways to do this is
A. 12 ways
B. 24 ways
C. 42 ways
D. 48 ways
As shown in Figure (1), 1 and 9 can only be placed as shown in the figure, then the position of 8 is as indicated by $*$, and the position of 2 is as indicated by。. This results in two scenarios, Figure (2) and Figure (3), where the position of 7 is as indicated by $\nabla$, and the position of 3 is as indicated by $\diamond$, each corresponding to 2 arrangements. In Figure (2.1), when $\nabla \diamond$ positions 3, the positions of 4 and 7 are fixed, at which point the positions of 5 and 6 have 2 possibilities; in Figure (2.2), when the positions of 3 and 7 are fixed, the positions of 4, 5, and 6 have 6 possibilities, so the arrangements corresponding to Figure (2) are $2(2 \times 2 + 6) = 20$.

In Figures (3.1) and (3.3), when the positions of 3 and 7 are fixed, Figure (3.1) has 1 arrangement, and Figure (3.3) has 6 arrangements; in Figure (3.2), when 3 and 7 are placed side by side, the position of 4 is fixed, at which point the positions of 5 and 6 have 2 possibilities, so the arrangements corresponding to Figure (3) are $2(1 + 6 + 2 \times 2) = 22$.
In summary, there are 42 arrangements that meet the requirements, so the answer is $C$.