Create automata from non regular grammar
Your first language isn't regular. Here is a simple way of showing this. Consider all words in your language of the form $a^*c^*$; if your language were regular, then so would be that language. However, the new language is generated by the grammar $L \to \epsilon \mid aLcc$ (this requires an argument), and so is $\{a^n (cc)^n : n \geq 0\}$, which is classically known to be irregular.

With more effort, you can show that your language consists of all words $w$ in which every proper prefix $x$ satisfies $\#_a(x) &gt; 2\#_c(x)$, and furthermore $\#_a(w) = 2\#_c(w)$.

An identical argument works for your second language. With more effort, you can show that the language consists of all words $w$ in which every prefix $x$ satisfies $\#_a(x) \geq 2\#_c(x)$, and furthermore $\#_a(w) = 2\#_c(w)$.

Summarizing, both of your languages are irregular, and this can be shown by intersecting them with $a^*c^*$.