Most likely the answer is no, sometimes a bios update can allow this, I also suspect if you're on a computer that only "supports" 4gb of ram then you are likely running a 32bit OS so even if it works you can still only use 4gb.
By the time you've done all of that, you could likely have bought a newer computer than you have for like $100 more, I wouldn't suggest it especially since its not even a given that it will take 6gb.