Will more RAM speed up my computer?

That is a high spec computer, it should not be running slow under that spec unless you have an awful lot of stuff running constantly off your drives, unless its not been well maintained or have viruses draining all the power out of it.. Upgrading to 12GB will definitely make a massive difference but 6GB is high enough for your system to work perfectly smoothly so something is causing it to slow, think you need to clean your drives and check all your system processes and program data usages, as well as making sure your security software is all running properly and is up to date. The graphics card could be pulling the system down a bit i would recommend an upgrade on that as if you regularly use photoshop and such software i can imagine graphics may struggle a bit there with that card, would be a nice addition to the rest of the powerful system spec you have. Also ddr3 ram has better power efficiency but without the psu spec stated here its hard to see whether you may need to upgrade the psu to support the extra ram, but ram doesnt use a great deal of power anyway so if you're upgrading im pretty sure it'll be fine. May be worth a bit of extra research, good luck :)