What type of rear derailleur is used on my bike?
I think that the model you have is 'hanger mount' as it mounts to a derailleur hanger built into the frame rather than being attached by an axle nut.

There are many Tourney rear derailleur models. All Tourney rear derailleurs are 6 and 7 speed compatible. You'll want a model with a long cage (SGS postfix on the model number).

The RD-TX800, RD-TY500 or RD-TY300 models should be drop in replacements.