What type of rear derailleur is used on my bike? Direct mount or hanger mount?

Sooo, one glance at these photos will tell you why I'm asking this...





Needles to say, I need a new one and I'd like to know what I should be looking for. It's for a 21-speed mountain bike, if it's of any importance. I hope you can make out anything from this mangled mess.
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.