Hey guys! What kind of rear derailleur is this?

Any cheap Shimano 8 speed or lower (derailleurs don’t really care) will work – the freewheel/casette looks rather narrow, but you need something with a capacity matching or exceeding the number of teeth on the biggest cog. My gut feeling is that pretty much anything you buy will be good enough: a Shimano Tourney RD-TX35 clears 34 teeth and you’ll struggle to find something cheaper from a name brand.

Importantly, it needs to match the shifters you have. They might be using standard shimano pull ratios, or it may be something else entirely. Or you’ll need to replace those as well, fortunately the low-speed shimano stuff costs next to nothing these days.