It is quite clear from the wording that there must be four of each sex at a table.

Here is a way to model this. Say that there is a lady A and a man X.

There are different grouping of four for A to be in.

That is, there are thirty-five pairing of four for the ladies.

That same logic holds for groups of four men containing X.

Now pair each female group containing A with a male group containing X.

Then pair each female group containing A with a male group not containing X.

How many such pairing do you get?

Is that the answer?