(A)It can't accept strings aab, aaab, aaaab.... which is accepted by given DFA.
So, we can eliminate this option.
(C)a*b(b*+aa*b) in this option first we can generate any number of a's after we can generate any numbers of b's or any number of a's is followed by a single b.
It can not generate string abbaabbb which can accept by given DFA.So, we can eliminate this option.
Answer should be both (B) and (D) here.