What is the maximum memory limit for a MacBook mid-2010 with the latest EFI and SMC updates?
If it's indeed the last model of white polycarbonate "unibody" MacBook that Apple made prior to the discontinuation of the MacBook (non-Pro/non-Air) lineup then it will actually support 16GB of RAM (2x8GB PC8500 DDR3 1066MHz SO-DIMM 204 Pin) and that's vouched for by the specs for that system in MacTracker as well as by the reliable folks at OWC.

You'll want to verify your exact model identifier via the System Information app though (this app also used to be called System Profiler in older versions of Mac OS X). 

Open up that application, select "Hardware" at the top of the sidebar pane, then look for "Model Identifier" on the right. If it reads MacBook7,1 and your "Processor Speed" is 2.4 GHz then you're good to go for 16GB of memory!