An even number of 0s (regular!)
Reverse mode — you defend.
Is L = { w ∈ {0,1}* : the number of 0s in w is even } regular?
You · move 1
You are defending L = { w ∈ {0,1}* : the number of 0s in w is even }. Claim a pumping length n — the engine will then choose a string and try to break your decomposition of it.