In the menu select Administration=>System Monitor. When the monitor window appears, click on the "system" tab. Your operating system will be right at the top of the page. If it is 32bit (x86) , it will be identified as "Release 6(felicia)" with the kernel version and the gnome version.
If it is the 64 bit version(x86_64) it will be identified as such. I deleted my 64 bit version several weeks ago and mislaid the live CD so I can't quote the exact identifier, but it will say 64 bit or x64.I believe the 64 bit version is also identified in the Grub boot menu.
This all assumes that you are using Mint 6 Main edition. If you are using the KDE, XFCE, or Fluxbox Community Edition, you have a 32 bit operating system as the CEs do not have 64 bit versions.
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