The bolts used to hold my back license plate broke off and part of them are stuck inside the holes-now what?

its called a screw extractor and you need a drill to use it. you can buy them at any hardware store and they're very cheap and easy to use. it uses a hardened drill bit to drill into the broken piece then the extractor grips the broken piece and pulls it out. my guess since its a license plate bolt is that the bolt is either 8mm or 5/16 roughly su you will need a 1/8 or 3/16 size screw extractor.

since its rusted try spraying some wd40 or penetrating oil on the bolt first and let it sit for a few minutes before you try this.

Licence Plate Bolts

Hold the plate in place where it is supposed to go and with a Sharpie mark the lower holes.Drill a small pilot hole at the 2 marks, through the metal.Bolt the plate on using self tapping sheet metal screws available at any hardware store.

Traditionally whenever we face a broken bolt, and if home remedies don't work, we drill a hole, convert it squarish by filing and drive in a square dive and take it out.

There is no scientific method available to solve this.

Drill some new holes and find some sort of bolt or one of those things you stick through drywall to make it hold tight.

Just get a very small nail and a small hammer and just back the nail out of the hole and replace with a different screw.