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According with the Intel website the processor supports 2GB of RAM unless the document is not correct but I doubt it.
Another possible thing is that the computer manufacturer have alter the features, incorporate customization and made other changes to the unit or built your system in a way that supports 4GB of RAM, in that case, your best contact support will be the computer manufacturer as they are more familiar with your system and how all the components interact with each other.
I found the answer in another thread. On page 115 in the full datasheet it says it can support 2Gb RAM with DDR3L-RS DRAM Device Technology but up to 8GB with LPDDR3 DRAM Device Technology.
As this is pretty wordy they write "Max Memory Size (dependent on memory type) 2GB" on the main specs page. I recommend they simply explain it on the main page it could be done with just a few extra words. I did wonder what (dependent on memory type) meant.
This says Z8000's are on either a T3 or T4 "Package Type". But although the Z8300 and Z8350 are both on the T3 package the Z8350 adds support for LPDDR3-1600 RAM.
So I'm guessing it is slightly different than the T3 chip? Or the CPU it's self changes the RAM support?
These screenshots are all from the official Intel.com datasheet but these two tables contradict each-other.
Well, Intel could list all of the possibilities, but I am afraid that that could cause even more confusion. It's tough when the design of the motherboard can make a difference to the limitation.
There are other similar cases. In some, for example, it is the difference between whether LPDDR3 and DDR4 memory is supported.
I could go either way with this. As a technologist, I would certainly prefer them to list all of the possibilities...