@HeadShot The language of second FA is L(M2)=a* and not empty
So if you draw the complete DFA you will see that if you take L(M1) U L(M2) THEN you will get DFA which will satisfy all the languages in {a,b} and if you take intersection of the same you will find that there is no language which satisfies a* and a*b is the resultant is empty
But the same is not true with NFA thats why the answer is option c
hope this helped :)