Decide whether this language is regular
The first step is to show that
$$
L \cap (aac)^*aabb^* = \{ (aac)^n aab b^n : n \geq 0 \}.
$$
Given that, you argue as follows: If $L$ were regular, then $L \cap (aac)^*aabb^*$ would also be regular. You can show in various ways that $\{ (aac)^n aab b^n : n \geq 0 \}$ isn't regular. It follows that $L$ isn't regular.