You need to understand the difference between an Update and an Upgrade.
An Update is a free change within an existing Operating System. Such as the .11 added to 10.4.
An Upgrade is a complete new Operating System that must be purchased. Such as 10.5 Leopard to 10.6 Snow Leopard.
Mac OS 10.6 Snow Leopard came out in July of 2009 and became obsolete in July of 2011 when 10.7 Lion was introduced. Unlike earlier Operating Systems which were removed from the Apple Store when a new OS came out Apple kept Snow Leopard around for a year until 10.8 Mountain Lion came out. When Mountain Lion came out they removed Snow Leopard and Lion from the online store.
The Early 2006 model 1,1 Core Duo can only run a maximum of 10.6 Snow Leopard. The models Late 2006 Core 2 Duos 2,1 through Early 2008 4,1 can only run a maximum of 10.7 Lion. The Late 2008 model 5,1 Aluminum Unibody through the Mid 2010 White Unibody model 7,1 can run 10.8 Mountain Lion.
The Snow Leopard 10.6 DVD should still be available from Apple for $20. You will have to call Apple Customer Care 1-800-692-7753 or 1-800-676-2775 to purchase it. It may still be in the Legacy Products list.
If they no longer have any in stock you will have to buy it from eBay or Apple resellers that still have stock. But you will have to pay a premium since the DVDs are no longer being made. Snow Leopard DVDs are already up to $100 on Amazon.