Mac Pro 3.33GHz 6-Core Intel Xeon & 10.6.8?

I suppose it depends on the age of the machine itself. Do you know when it was purchased? Do you have installation disks?

I would think that Snow Leopard 10.6.8 would work on a 2010 version of this machine as that was the OS X version that it originally shipped with.

I don't think they've changed the quad core mac pro since 2010 (even though it's called a 2012 now). It might be possible that a newer one will only run more recent versions of OS X. It's hard to say since this same configuration has been available for such a long time now.

Just try installing 10.6.8 from a flash drive or disk. The installer should let you know whether or not you can install it.

Why? What trouble are you having? It will but not from retail 10.6 DVDs

You might want to use this and link to it

http://support.apple.com/kb/HT1159

Changes in firmware pretty much 'say' what build version you can use.