This automaton will have 3 as the minimum number of states.
Your problem statement is $n_a(w) \equiv2mod3$ which is same as saying $n_a(w)mod3=2$
There will be three equivalence classes in which this DFA would divide your input into.
Class 0: All such strings with $n_a(w)mod3=0$
Class 1: $n_a(w)mod3=1$
Clas 2: $n_a(w)mod3=2$