Officially, P6100 supports 8GB although HM55 Express technically supports 16GB. But the CPU is socketed and back in the day it was very popular to change the CPU in HM55 laptops to a 45nm Clarksfield i7 such as i7-720QM (which boosts to 2.8GHz), and then 16GB of DDR3-1333 which worked fine even if not officially supported
So I would suggest changing the CPU (and thus the memory controller) first to the one you wish to use, and then bring the laptop down to your local used computer store and try the memory before you buy it, because it's not just what the hardware supports but the BIOS too
As this is from before Haswell, only up to 4Mbit DDR3 chips can be used so any 8GB stick must be low-density and thus have 16 chips on it. 4GB sticks can have 8 chips, or even lower density 16 2Mbit chips suitable for Core 2 should work also. To further add to the confusion, 12 years ago the 2Mbit chips were considered low-density while vintage RAM with 4Mbit chips may actually have high-density printed on them, while today 8Mbit is considered high-density. So don't go by just density claims as that's relative to what was available at the time
Haswell required DDR3L and there were even memory controller failures reported from running high-voltage memory on them. But DDR3L is required by spec to also be able to operate at 1.5v. And memory voltage or timing settings are very rare in a laptop, so it either works or it doesn't.