Either construct NFA and then convert it into DFA. Or If you want to construct directly then here is the Idea :
While constructing DFA, Whenever you see $a$, think of it as 2nd last symbol. So, After this $a$ you can allow $a,b$ and accept. But after this when you see $a,b$ you must make a transition to relevant state.
The DFA will look like this :
its really great thanks