'000' cannot be accepted. So, '00' when gets another 0 must go to a dead state, q.
So, options A and B are eliminated.
By analyzing options C and D, we can understand that when states like 00, 01, 11 or 10 get an input 1 or 0, the next state is the last two digits of the newly formed string.
11 +0 -> 110 (So, 11 on 0 goes to 10).
01+1 -> 011 (So, 01 on 1 goes to 11).
So option D is correct.