The question is about the number of ways the invitations can be distributed among boys and girls in different ways. Amit and his wife have 2 possible patterns of inviting friends: Amit can invite 2 boys and the wife invites 2 girls, or Amit can invite 2 girls and his wife invites 2 boys.

In the first case, Amit can invite 2 boys from 2 in C(2,2) = 1 way and his wife can invite 2 girls from 2 in C(2,2) = 1 way. And in the second case, Amit can invite 2 ladies from 3 in C(3,2) = 3 ways, and his wife can invite 2 boys from 3 in "3 choose 2" ways i.e., C(3,2) = 3 ways.

Therefore total number of ways = 2* (1*1 + 3*3 ) = 2*(1+9) = 2*10 = 20.

Option 3 (46) is the provided answer but it doesn`t align with the explanation. Therefore, alert - correct answer should be none of the given options.