My initial thought is that L can't be context free since I can use the pumping lemma. I also don't think a grammar can be generated since it needs to keep track of the number of c's and a's. However, I'm having a hard time coming up with an algorithm for this language.
Here's a hint:
- Could you make a grammar for $a^nb^n$, $n\ge 0$?
- Could you make a grammar for $b^mc^m$, $m\ge 0$?
- Could you make a production that concatenates the languages in (1) and (2) above?