want to upgrade my osx 10.5.8 to 10.6.8 or higher, can I do it ?

Yes, if you have 1GB or more of memory, you can upgrade to OS X 10.6.8. Call the online Apple store, which in the US is at 800-MY-APPLE to order OS X 10.6. Many have been upgrading in order to install iTunes 10.7.

If you have an Intel Core 2 Duo processor and 2GB memory, with 4GB recommended, you can upgrade to OS X 10.7 Lion by calling the online Apple store, who will email you a code to download from the App store. You need to be at OS X 10.6.6 or later to use the App store.

Do this first...

Check that your Mac meets the System Requirements for Snow Leopard...

Snow Leopard Tech Specs

http://support.apple.com/kb/SP575

If so... Purchase a Snow Leopard Install Disc...

http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard

Other countries...

http://support.apple.com/kb/HE57

After the Successful Install, run Software Update to get the latest updates for Snow Leopard.

Be sure to make a Backup of your Current System Before Upgrading...