Formal definition of a language accepted by PDA
I would say it's $L(A)=\{a^n c^m b^{2n}| n,m \in \mathbb{N}, m \geq 2\}$

For every a push 2 zeros on the stack, so it's for now just called a^n. 
The number of c's is m, because it is not related to the number of a's. You can accept any number of c's (larger than 2) no matter how many a's were there.
The number of b's is twice the number of a's because you accept for every 0 on the stack 1 b, but wrote twice 0 for every a on the stack.

In fact the language $L(A)=\{a^n c^n b^n| n \in \mathbb{N}\}$ can't be accepted by any PDA, but only a linear bounded automate(LBA) or a Turingmachine (or other similar models) The reasoning is that if you count the number of a's and want to have the same number of c's and b's later(not mixed) your stack will be empty after you sucessfully counted all the c's and the PDA will have forgotten the number to check whether the b's appear in this number.