So far I have reached to this solution:

1) There are total 30C2 pairs. = 435

2) If every senator has 6 enemies then 30 senators will have total 30*60/2 enemies pairs (removing double counted ) = 90

3) Total friend pairs are 435 - 90 = 345

For choosing committees, we have to choose to choose 3 pairs from 90 an then 3 pars from 345 such that each node of pairs is shared with another node. But how, can't get this.

Any other way to look at this problem?