Hello vitaliy295,
To help us better assist you, can you let us know more about what happens when you try to download music for offline listening? For example, do you receive an error message? If so, what does the error say?
The above information will help us proceed.
Please also be sure to review all of the information outlined in the link you came from, to ensure the correct process is being used to download music: Add and download music from Apple Music
How to add music from Apple Music on your iPhone, iPad, or Android
1. Open the Apple Music app.
2. Touch and hold a song, album, or playlist that you want to add to your library.
3. Tap Add to Library.

Thanks!