How to upgrade my Mac Pro to an OS newer than 10.6.8?
It sounds like your Mac Pro is not supported (too old?) by a newer OS than 10.6.8.

Check by looking in the System Information app, to see what version of Mac Pro it is. Supported versions are "MacPro3,1" or greater. Unsupported versions are MacPro1,1 or MacPro2,1.

The reason why the older models are not supported is not arbitrary - it's because the first models had a 32-bit EFI, and the later ones have a 64-bit EFI. The later operating systems require a 64-bit EFI.