what beats solo hd work on ipod shuffle 4th generation?

It should work. Maybe they left it off (also the iPod shuffle 3rd gen) because the headphones do not have the control buttons on the cord, and the 3rd gen and 4th gen shuffles can use those buttons. But the 4th gen (unlike the 3rd gen) shuffle also has control buttons on the iPod itself, so you can still control playback without buttons on the cord (although having those cord buttons would be useful because it iPod is so tiny).

Are you sure you want to buy $200 headphones for a $50 player? 😉

An iPod shuffle is meant to be a low-cost "casual" iPod that people clip on their clothes, and do things like go to the gym. An iPod nano may be a better fit for use with high-end headphones.

It has a screen, so you don't have to use VoiceOver to get the song info and navigate your playlists; you can just use the touchscreen. It has more storage capacity, 4 or 8 times more than a shuffle. It has longer battery life per charge. It doubles as your watch. And it's still not too much larger than an iPod shuffle, and the current version of the nano is focused on audio only (no video playback).

Yup... I understand. I have nothing against shuffles. I have a few myself (including a 1st gen white one which has VERY GOOD sound), and they are actually my most-used iPods, because they are so convenient. But I use mine with headphones that cost less that $20 (they still sound pretty good to me), so I can go running with them, wear them on the bus/train, and not care if I mess them up. And sound quality is not the top concern, because there is a lot of noise around me.

If I had big $200 headphones, I'd use it with an iPod that I knew could take full advantage of the better sound quality they provide.

FYI - You can get a Apple Certified Refurb iPod nano for $99.

http://store.apple.com/us/browse/home/specialdeals/ipod