how do i find my multiplayer key for world of conflict i have bought please

Click your user name in the bar at the top of the web page. Navigate to World In Conflict on the shelf. Click it, click more and select "Serial Keys".

Sometimes GoG has run out - if that's the case it will say something like "depleted" and you'll need to contact support.

In case it's not clear, you need to do this while logged in using a web browser.

Actually don't click on your user name, but over over it, then select "Games".

Clicking it would show the profile page.

Unless, like me, you have no profile.

(They finally fixed the "takes you to a non-existent page" bug for users without them)