There are N vertices of the 24-cube which have a 1 in the ith coordinate and a total of five 1s.
We adopt the convention that the first coordinate i increases as one goes downwards, and the second coordinate j increases as one goes from left to right.
Now X can be taken as coordinate variable on M.
This explains why we chose 9 rather than, say, 1 for the second coordinate.
Keep only those vertices whose coordinates sum to 4.