First they should have to mentioned start state here I assuming X as a start state because x is only state from which all other state are reachable, minimum length string generate by x is a
X->Y
Y-> A from here itself we can say answer is b
Now state X and Y assure that already one a is extra either at beginning or end or both side
State S,A,B ensure number of a= number of b
S,A,B cannot be reached without X hence option b is correct