So as we can see we have an NFA for the given regex. Try to apply the following three algorithms to get the desired result.
- Removal of $\epsilon$ moves to obtain $\epsilon$ free NFA.
- NFA to DFA conversion.
- DFA minimization.
Give it a try. If you are not sure with what you obtain, share it as an edit to your question.
EDIT
Here I see my approach was not really appreciated. So here is an equivalent DFA -
P.S This isn't minimized DFA.
HTH