Why can't my iphone 6 connect to itunes on mac osx 10.6.8

The minimum version of iTunes for a device is running iOS 11 is iTunes 12.6.3.6. The last version of iTunes to run on Snow Leopard is 11.4.

A potential workaround to get music to your device without upgrading your computer would be to take out a subscription to iTunes Match. See Subscribe to iTunes Match - Apple Support for details.

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Because your version of OSX is too old to support the version of iTunes required to connect to an iPhone 6. We would need more information about your computer and system software plus the phone's system version in order to see if you can possibly upgrade.