OS10.6.8 and iphone 6s. itunes 11.4 not compatible

You need a newer version of iTunes.

When I check my iTunes (11.4) it says there is no newer version..?

Well yes of course a Mac running OS 10.6.8 will show that iTunes 11.4 is the highest that you can get and there is no newer version for that OS, because there is not.

Also, NO you are NOT running the latest software on both ends if you are still using OS 10.6.8. The latest OS for Mac is El Capitan which is OS 10.11.1.

You need to update the OS on your Mac to be able to get the latest version of iTunes or you cannot sync your iPhone 6 with it - not compatible.

Update your software or you will not be able to use your iPhone.