DFA for exactly two of a and one or more of b
Since it's for class, I won't actually build the DFA for you, but I will give you a way to look at it that'll help.


As far as $b$s go, you really only care about whether or not you've seen a $b$ so far in the string.
As for $a$s, you care about whether you've seen 0, 1, 2, or more.


Each combination of scenarios for both letters (like "seen none of either" or "seen one of each" or "seen one $a$ and no $b$s") changes in its own way depending on whether you read another $a$ or $b$. How might you express that in a DFA?