DFA: Union

Hi.

I’m actually taking one class right now, if you know about DFA’s, you may be able to help me out.

1st language: {w|w has exactly two a’s} //This has 4 states.
2nd language: {w|w has at least two b’s} //This has 3 states.

Making DFA for each is very easy, but I have no idea how to combine them so that the language becomes {w|w has exactly two a’s and at least two b’s} //Which should have 12 states.

Sigma (the language) = {a,b}

I have the answer from the book, but the book has no explanation as to how they got that… (Book sucks!)

Thanks!