TLDR: If you’re on Windows, probably here:
C:\ProgramData\Blackmagic Design\DaVinci Resolve\Support\Resolve Disk Database\Resolve Projects\Users\guest\Projects.

Please note that your system drive may not be ‘C’, and the user may instead be ‘admin’, presumably if running Resolve as an administrative Windows user.

Now, if you’re hoping to get back an old copy since closing auto-saved unwanted changes then you may be out of luck. Unless that drive has file versioning turned on, or you had already enabled Davinci “Project backups” from “Preferences” -> “User” -> “Project Save and Load”, or you had exported the project earlier.

Still, with this knowledge you can prevent data loss in the future by enabling Davinci “Project backups”, enabling file versioning of your drive in the OS, and/or moving the containing folder to a cloud-synced-folder-with-versions like DropBox; then sym-link the moved folder back to the original location.

Another fun fact, the .db files found therein are SQLite databases, which allows you to peek inside with a variety of different tools.