Can I add more memory to my Mac OS X version 10.6.8

Choose About this Mac from the Apple menu, click the version twice, append the last three characters of its serial number to http://www.everymac.com/ultimate-mac-lookup/?search_keywords= , and load the page. This will reveal how much RAM can be installed in the computer and what specifications it needs to have.

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If I'm not mistaken (I've been known to be that on hardware issues...), 4Gb in dual-channel is the limit, with each slot accepting 2Gb max.

The 2 places I’ve seen recommended most to buy reliable RAM are below. I have purchased RAM several times from Other World Computing and have always been very satisfied with the product and service. They have on-line instructions on how to replace the RAM. OWC has also tested RAM above what Apple states is the maximum. I now have 6GB installed on a machine supposedly limited to 4 GB.

Crucial

Other World Computing