Always before the verb Javi. He doesn't even know how to tell the time yet. She can't even drive properly. We couldn't even find the way to the coffee shop. I can't even think of any more examples ... :-)

I believe they mean the same thing however the first sentence is what natives would use and is grammatically correct. The second sentence isn't grammatically correct , so don't use that one! Happy learning!

In your second version, the 'even' would relate to the noun, not the verb. Even cookies and even tigers don't make sense, which is why they are wrong. They are not grammatically wrong, they are logically wrong. You could say "She doesn't like even numbers", (she doesn't like 2,4,6) or "He wants even piles of leaves". That is obviously a completely different meaning.