A Possible Compatibilist Argument

Question:  What would be the argument of a compatibilist? In other words, how do they go about arguing that determinism can coexist with free will?

In response to this question, I suppose a compatibilist would argue that determinism and free will coexist because even if determinism is true, the illusion of free will still affects humans anyway. In my opinion, this would not mean that free will and determinism coexist. It just would mean that the illusion of free will coexists with determinism. As I said in my Q&A response, the fact that free will is just an illusion means that free will itself does not really exist, making it unable to coexist with determinism, because determinism cannot coexist with something that does not really exist itself. However, I consider myself an imcompatibilist, and a determinist, so my response is biased. So, I guess one approach a compatibilist could take to respond to my question is that free will coexists with determinism because humans seem to naturally feel a sense of free will, even if they agree with determinism.