Subscriptions won't come up how would they know them from an unknown connection.
The idea is you input the email you used when getting the trial subscription and the subscriptions that you had in your image.
The first link is a general FAQ one and select the option that is closest to what you are trying to achieve. Or other help suggestions.
As for the subscriptions not showing they should assuming that you used the same email address in your avast account.
I don't know if the free trial shows up in your account, I guess the free trial is different as you haven't yet paid for a subscription.
As an Avast Free User I have never had to do this so I'm working blind.
EDIT: Another link for you to try -
https://support.avast.com/en-en/article/35#idt_010 - but as I already said this is going to rely on the email used when getting the trial version/s being the same.