Forgotten Master Password

I’ve forgotten my master password but I can access Avast Password via fingerprint. How does sync work for me since I can’t remember my master password?

The master password protects main secret which is unique per each password storage while other login methods as well as finger print is doing the same so if you have an option (any of supported) which unlocks the password storage (means it can unlock main secret) then the synchronization still can and will work.

So if my phone breaks or I buy a new one, how will I be able to transfer my passwords over to my new device?

Won’t I be asked for my master password?

What about synchronising to my Avast account? Won’t I be asked for my master password when I attempt to do so?

Best advice, start all over again and this time , remember that master password.
The sooner you do it, the easier it will be. Eventually you’ll need to do that anyway so get it over with.

No need I have turned my house upside down and found the piece of paper I wrote the password on. So what’s next? How to sync from Avast Password to my Avast account?

Follow this guide
https://support.avast.com/en-ww/article/Synchronize-Passwords-across-devices