So, if the game is installed, and assuming you actually bought it and used the cd key the first time it may be stored on your computer still.
1. Try Belarc Advisor, it will retrieve all the CDkeys it can find records for on your computer and list them for you:
http://www.belarc.com/free_download.html
2. You can also try Magic Jellybean KeyFinder:
https://www.magicaljellybean.com/keyfinder/
If either of those is successful, you can likely add RE6 to your steam account so you can always redownload it:
https://support.steampowered.com/kb_article.php?ref=5414-TFBN-1352
If all that fails, buy it again:
http://store.steampowered.com/agecheck/app/221040/