It MAY work with 6 or 8 GB, but there may be unexpected issues. Personally, I'd recommend saving up and replacing the motherboard, CPU, and memory, but you should be able to find a motherboard that supports that CPU and more RAM if you go used.
If you're running a 32 bit OS, it will never go above 4GB so you would be essentially wasting money. Also, a Dual core to my knowledge does not take advantage of 8GBDDR2 RAM. If it does, I believe your e4600 2.4 would be severely bottle-necked. Good luck!