How to draw a DFA for given language?

Question

Give a finite state diagram for a DFA that accepts any word in the language $L = \{w \mid w \in \{a, b\}^* \text{ and }w \text{ alternates } a\text{'s and }b\text{’s and has an even number of }b\text{’s}\}$.

My attempt: I am having problem on how to deal with the even part of b.