Q: In the App Store, I click on "get" Yosemite, I receive this message, "We could not complete your purchase. This version of OS X 10.10 cannot be installed on this computer." I meet the requirements: I have,MacPro(Early 2008), 10.6.8....

What's the Model Identifier on your Mac Pro?

It's your processors... the Early 2008 Mac Pro doesn't ship with 2.66GHz Processors, thus your model is too old.

Your processor specs indicate its a 2006 Mac Pro. Not a 2008.   Thus Yosemite is not supported. You should still be able to update to Lion.  Not Mountain Lion though.

Since the 2009 Mac Pro (4,1) was also available with the 2.66GHz processors, is eligible for Yosemite and the OP described his Mac as "(Early 2008 or newer)" in the post, which meets the requirements, the Model Identifier would be definitive. I also suspect he has the 1,1 Mac Pro but the Model Identifier would tell us for sure.

The 2009 had quad-core processors, he said his were dual-core... hence his machine is an earlier model than the Early 2008.

Check that your computer is compatible with Mountain Lion/Mavericks/Yosemite.

To check the model number hold down the option/alt key, go to the Apple menu and select System Information.

Yes, that model identifier is for a 2006 Mac Pro.

How to identify Mac Pro models - Apple Support