You can use the offline features of your paid membership on up to 10 mobile devices at a time. If you try to download a video on a new device once you've reach this limit, the oldest of the 10 devices will be de-authorized. You can do this up to 4 times in one year.
After you’ve made your 4th swap, you'll see the message "Sorry, this video can't be taken offline." This message means you’ve hit the limit of devices you can use to download. You can't download videos on any new devices until the limit resets. You can continue to use YouTube Premium to download videos on any device you've used previously.
Note: You can also view and manage your devices in your Google Play Music account settings.