how can I upgrade mac os x 10.6.8 to 10.10.5 or later?

IF your Mac meets the minimum requirements you can upgrade to El Capitan How to download OS X El Capitan - Apple Support and then possibly High Sierra How to download macOS High Sierra - Apple Support

Be advised that some of your applications that run under Snow Leopard will not work after the upgrade and the ram requirements for the newer OS is more demanding, you'll possibly need to upgrade your ram.

Check for 3rd party software compatibility: RoaringApps

if your mac only has 4gb memory you should consider upgrading the memory if possible, or things could take a turn for the slower in terms of responsivity of your computer.