What is the best OS I can run on a 3.06 GHz Intel Core 2 Duo with 2 GB 800 MHz DDR2 SDRAM computer?

Bbefore doing anything with whatever Mac OS X you now have, you need to raise the memory level to at least 4 GB - all OS X version from Lion, 10.7.5 onward need at least 4 GB to run well. See what is offered at OWC http://www.macsales.com or Crucialhttp://www.crucial.com for quality, guaranteed to work memory.

Then you can decide on OS X upgrade. If your Mac is on the list of compatible hardware, http://www.apple.com/osx/specs you can go to Yosemite if you have Snow Leopard, 10.6.8.

At least Yosemite, but you should install more RAM in it prior to upgrading it past 10.6.8.

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All of the 3.06GHz Macs are capable of running Yosemite.

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