Yesterday i decided to download and play fallout new vegas wich i got from amazon prime long a go but in gog galaxy it apears that i dont have any game, how can i fix this?

I'll just be the one:
Are you really really (and please double check) really really sure that you are using the right account?
The account you use for posting seems to own 3 games. Make sure you use this one to download your games.

An alternative would be not to use Galaxy at all and just download the games from the website with the account you are logged in with.

1. Click the cogwheel in the top left and choose Exit.
2. Start File Explorer and go to %ProgramData%\GOG.com\ in the address bar.
3. Move the Galaxy folder somewhere like the desktop.
4. When you next start GOG Galaxy, you'll be prompted to log in, after which it will import your list of owned games. If that doesn't fix it, there may be something wrong server-side and you'll have to open a support ticket.

If you want to use offline installers, log into the site using a web browser, then hover over the menu at the top and choose Games to go to your library. From there, click a game, then ignore the blue button and expand the Backup Offline Installers section to reveal the download links.
Games installed via offline installers can be added to GOG Galaxy: click the cogwheel, choose Add Games & Friends, then Scan Folders for GOG Games. But I don't know if features like achievements and cloud saves would work if you don't first resolve the issue of the games not being recognized as owned.

If it was long ago, then seeing as this account you used for posting has only existed since September last year, I'm not surprised you cannot find your game listed in it.

Was this a game you got a GOG redeem key for at Amazon Prime?
If so, then usually they have a time limit to redeem, and to redeem you would have needed a GOG account.
Did you have and do that?

If so, then likely you used a different account to this one, which by the way is against the rules ... but hey maybe you forgot that account existed. If so, check your emails and contact GOG to fix, if needed.

@OP.

Your profile says it has 3 games. Is Fallout NV included as one of these three?

"Fallout: New Vegas" was on offer via Amazon Prime in October 2022.

They said long ago, and long ago to my mind is not just October last year, hence why I mentioned September when the account was created. Now if they has said a while ago, then yes, sometime after creating their account.