You need to give the model number of your computer in order for people to really answer that question. What you did tell us, is that you are (probably) running DDR-2 memory and that your motherboard would be able to use up to 4200 speed mem as an upgrade.
Look at the different speeds:
DDR2 3200 = 400Mhz
DDR2-4200 = 533Mhz
DDR2-5300 = 667Mhz
DDR2-6400 = 800Mhz
The answer (without knowing more about your computer) is MAYBE you can run DDR2-6400, the socket is the same, so the memory will fit in the same place as your current memory. It is true that DDR2 was designed to be backward compatible; but, not all memory is the same. PC6400 is the fastest and sometimes requires more voltage than your motherboard can supply. If the sticks of RAM you are looking at specify they will run at 1.8V; then they will probably work in your motherboard; but, you will not get much of a performance difference because your motherboard will run the RAM at a slower speed than PC6400. Try to find PC-4200 if you need more in your machine. It is getting really cheap now.