How do I transfer 3rd party music on a 6th gen iPad to a new 8th gen iPad?

Any Music/Media content from CD and external sources must be transferred from your PC/Mac using iTunes (or Finder on later Mac computers). “Paid” material from the Apple iTunes service can be simply downloaded to your iPad from Apple iTunes.

The iTunes Application on your PC/Mac maintains an authorised copy your media library - whether this material is loaded from a CD, or downloaded from the Apple iTunes Service - and media derived from this library can be transferred to your iThings. These support pages provide more details:

Sync your iPhone, iPad, or iPod using your computer - Apple Support

iTunes - Apple (UK)