How much RAM can my computer hold?

Ok im confused on how much RAM i can put in my computer ...
I have an Emachines ET 1831 Desktop and theres already 4 GB
and reading specs online ,some places say i can only have 4 GB of Ram ,But also read elsewhere that if i have a 64 bit OS then i can have up to 16 GB of RAM!
whould anyone know for sure if i can install more RAM .. its a 2 slot system .. so was thinking ID like to throw in 2 4GB sticks in ...
 
Seems like most of the motherboards that use that chipset are limited to 4GB.
 
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