Every member of the family gives a gift to every other member of the family. there are ten members this year. if there are just 2 members exchanging gifts, how many gifts will be exchanged

The statement is contradictory, because it is said that every member of the family gives a gift to every other member of the family. And from 10 members, there are just 2 exchanging. Anyway, maybe they are only 2 members exchanging the gifts at that point in time.
So, each member will exchange 9 gifts (that is 10 members total minus herself), and 2 members are exchanging gifts at that point, so 18 gifts are being exchanged.