A cpu does not define the max memory size, it is the motherboard that does.
What is the make/model of your motherboard?
I have little doubt that you can run at least 16gb which is normally plenty.
Thank you all for the responses. I will have to get the model # when I get home from work. I do have 4 slots total, and I have 2 sticks of 4gb ram that I will install to give 16 total.