A few things comes to mind...
1. You are not using a 64-bit operating system, but a 32-bit operating system which generally recognizes up to 3.3GB of RAM.
2. If #1 is the case, then internal graphic core may be somehow using 1+ GB of system RAM for whatever reason.
3. 6GB = 4GB stick + 2GB stick. Perhaps the 4GB stick is defective.