Yeah... Why would you still be running 10.6.4?
I don't know for sure the exact state of support in MC20 for Snow Leopard. I know from the very first OSX build of MC, they recommended Lion or newer, and I think there was some talk of dropping Snow Leopard entirely.
But, certainly your only chance is to run the latest version of Snow Leopard.
And, your Mini can run both
Yosemite and Mavericks (whichever you choose), and the upgrades are free, so there's no real reason you
can't upgrade your OS all the way current. Yosemite would probably run better on it (it has less chrome), even, and you'll get security updates.
Getting Mavericks would be a little more complicated, because they don't offer it in the Mac App Store anymore, but you can probably find it out there on the Interwebs if you really would prefer not to go to the current OS. In any case, you shouldn't stick to 10.6.4 certainly.