I want to hang my fire extinguisher on the cabinet next to my sink. Below are pictures of the fire extinguisher bracket and the location where I want to put it. Should I use a bolt with a nut - or some sort of screw?



I want to hang my fire extinguisher on the cabinet next to my sink. Below are pictures of the fire extinguisher bracket and the location where I want to put it. Should I use a bolt with a nut - or some sort of screw?



Probably too heavy for wood screws into chipboard cabinets.
If the screws don't work then a couple of bolts with penny washers.
The extinguisher looks a bit battered, you should check the trigger mechanism looks ok. BUT don't try and squirt it a little bit - the cooling gas can make ice form in the valve and stop it turning off
It looks like the holes on the mounting bracket are shaped for a bugle head, which AFAIK limits you to using a screw. (Well, you could use a bolt, but the head would push the extinguisher out so that it's not parallel to the cabinet face which would look untidy, IMO.)
If your cabinets are 3/4" plywood, the screws probably all you need. If they're made from particleboard, you should add some reinforcement in the form of extra wood to hold onto: glue a piece of plywood to the inside of the cabinet and screw into that. Most cabinets that I've seen have a lip around the front edges, so if you use a piece that doesn't protrude past that lip and fills the full depth of the cabinet and the height between the shelves, it'll be less noticeable.