Not possible until you have at least upgraded to Snow Leopard 10.6.8 because you need it to access the App Store where you will purchase and download Mountain Lion when it is released.
Upgrading to Mountain Lion
You can upgrade to Mountain Lion from Lion or directly from Snow Leopard. Mountain Lion can be downloaded from the Mac App Store for $19.00. To access the App Store you must have Snow Leopard 10.6.6 or later installed.
Be sure your computer meets the minimum requirements:
Apple - OS X Mountain Lion - Read the technical specifications.
Macs that are NOT expected to support OS X Mountain Lion
Older Macs and those with weaker GPU’s will likely be left behind:
- Anything with an Intel GMA 950 or x3100 integrated graphics card
- Anything with an ATI Radeon X1600
- MacBook models released prior to 2008
- Mac Mini released prior to 2007
- iMac models released prior to 2007
- Original MacBook Air
Your model must have a 64-bit EFI boot ROM. See OS X v10.6- Macs that use the 64-bit kernel
An easy way to tell if you are running a 64-bit kernel is to use the uname command-line program. Open the Terminal in the Utilities folder and enter the command line:
$ uname -a
Press RETURN.
The "x86_64" in the excerpt below means that you are running a 64-bit kernel. If the output showed "i386" instead, that would mean a 32-bit kernel.
$ Darwin... root:xnu-1456.1.25~1/RELEASE_X86_64 x86_64
If your computer does not boot into the 64-bit kernel automatically you can force it to by restarting and holding down the "6" and "4" keys after the chime. Re-run the above command in Terminal. If you don't see "x86_64" then your model does not have a 64-bit EFI boot ROM and cannot boot Mountain Lion.
Are my applications compatible?
See App Compatibility Table - RoaringApps - App compatibility and feature support for OS X & iOS.
Am I eligible for the free upgrade?
See Apple - Free OS X Mountain Lion upgrade Program.