Your iMac supports Snow Leopard.
Snow Leopard is not available as a download. You need to order the installation disk from the online Apple Store ($20 with shipping).
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Once you have Snow Leopard installed and have done Software Update to bring it to OS 10.6.8, you will have the App Store app. The App Store app allows one to download and install OS 10.7, OS 10.8, or OS 10.9. (Note: OS 10.7 and OS 10.8 require purchase of a code from the online Apple Store. The code allows one to download and install through the App Store app.)
Please note for iMacs with Intel Duo Core 2 Processors:
OS 10.6 is maximum OS supported by the mid-2006 iMac (ID iMac4,2)
OS 10.7 is maximum OS supported by late-2006 iMacs (ID iMac5,1 iMac5,2 iMac6,1)
OS 10.8 & OS 10.9 are supported by mid-2007 and later iMacs (ID iMac7,1 and later)
(Model IDs are found in “About This Mac” –> “More Info” –> “System Report”)
