Do most/all of the Sony NEX lenses interchange with the Sony Alpha's (A6000 specifically). I am looking at a 420-1600mm super telephoto lens. Thanks for any help you give
Lenses are interchangeable if they are made for the same mount and cover at least the imaging circle of the camera.
Unfortunately, Sony offers a lot of combinations and has even changed naming recently. They have 2 mounts, E-mount and A-mount. Both of these have APS-C or Full-Frame coverage, so there are in all 4 combinations (APS-C A-mount, Full-Frame A-Mount, APS-C E-Mount Full-Frame E-Mount).
The Sony Alpha A6000 has an E-mount and APS-C sensor, so you can give it directly any lens made for E-mount.
Since the E-mount has a shorter flange distance than the A-mount and are designed to adaptable, you can also use an adapter to mount any A-mount lens. Depending on the combination of lens and adapter, you may or may not have autofocus capability.
Also since you are considering a telephoto lens, it is important to know that stabilization will only be provided by the lens and, with very few exceptions, A-mount lenses are not stabilized since the body usually does the job. So, going the A-mount adapter route is less desirable.
As long as the lens is a Sony E mount mirrorless lens, it should mount and be usable from the A6000. Sony A-mount dSLR/dSLT lenses, however, will require an adapter. There's a little confusion over the names, since Sony used to call their dSLR/dSLT system "Alpha" and their mirrorless system "NEX", but they've since decided to umbrella all their cameras under the Alpha name. If the lens is designated as NEX or "e-mount", that's what you're looking for with a Sony mirrorless camera.
However. That specific lens you're probably looking at, the $200 Opteka/Kenko 420-1600mm lens is a different kettle of fish. It's actually a T-mount lens, and you're using it not only with a mount adapter (which is why it can be fitted to a wide variety of mounts), it also uses a 2x teleconverter (it's actually a 210-800 lens), and has a maximum aperture of f/16. It's basically a cheap plastic telescope you can put on your camera. It doesn't autofocus. Don't expect to handhold this lens except in very bright sunlight. Don't expect to get tack sharp images with it.