The total number of guests present at party was 77 out of which 40 liked dancing, 23 liked swimming and 6 liked both. So, the number of guests who like only dancing and only swimming would be $$(40-6)=34 \&(23-6)=17$$ respectively.

Nothing is said about the number of people who neither liked swimming nor dancing, we have assumed it 0 .

So, the number of guests who like only Dancing $$=40-6=34$$.

Hence the answer is (D).