4. (8 points) Fill the numbers $1-9$ into a $3 \times 3$ table, such that in the same row, the number on the right is greater than the number on the left; and in the same column, the number below is greater than the number above. Given that $1,4,9$ are already filled in, how many different ways can the remaining 6 integers be filled in? $\qquad$
【Solution】Solution: 2 or 3 can only be filled in the 4 cells at the top left,
There are 4 numbers left, choose any two to fill in the bottom left, the smaller one on the left, and the remaining two in the top right, the larger one below, which completes the task. There are $C_{4}^{2}=6$ ways to fill,

Therefore, according to the multiplication principle, there are a total of $2 \times 6=12$ ways to fill. The answer is 12.