This is an old rear derailer pulled off of a Trek 820 entry level mountain bike.
The derailer has some surface rust on the bottom of the cage, and some rust stains on the pulleys due to a super rusty chain. But all parts move nice and freely. The bike this came off of had a 3x7 drivetrain.
According to a google search, it looks like this is compatible with 7 or 8 speed cassetts with a max cog size of 34 tooth.