|"Actually when i check my system information it is showing 4 GB. "|
That may be shown in mb, not gb - there are 1,024 mb per gb, in the binary way of stating the memory size that the operating system uses, so 4gb = 4,096mb
The Total Physical Memory amount shown there is the amount of ram installed on the mboard that's reported by the mboard's bios. Some bioses report the total amount of memory installed even when you're using onboard video - some subtract the amount used by onboard video when you're using onboard video, some subtract 1mb from the amount for the conventional memory amount that can't be made available to the user.
"I have only ever used the 32-bit edition and it has always registered my 6gb of ram "
You can install more than 4gb on most recent mboards, but when you have a 32 bit operating system, it's limited to a 4gb max virtual memory address limit in Windows, for both the installed ram and what the operating system requires, not just the ram. E.g. In this case, you would still have the max 2.96 gb figure in Windows you have now, for the same video situation on the same mboard with the same programs running.
Onboard video is a video (display; graphics) adapter built into the mboard - it's usually built into one of the chips in the mboard's main chipset - it's not removable like a video adapter on a card installed in a slot is - it has no ram of it's own on modern mboards, so it shares part of the ram installed in the mboard.
Most laptops have onboard video.
Some desktop computers have onboard video
On a desktop computer, the monitor port or ports for onboard video are in the same I/O area (~ 2" x 6") on ATX mboards as most of, if not all of, the other ports are in on the back of the computer case. A monitor port or ports in a slot space by itself at the back of the case is for a video card that has been installed in a slot on the mboard.
In most cases, when an AGP or PCI-E X16 video card has been installed in a slot, the onboard video is automatically disabled and no longer shares the ram installed on the mboard.
A video card installed in a mboard slot always has it's own ram.