I have a Canon NP 6412F copier that appears to have a broken piece at the back of the toner cartridge. The cartridge is loose and it obstructs the closing of the machine. Is this something that can be fixed?

check cartridge setting how-
check all spring on correct place
check ITR spring touch point
check printer to cartridge touch point

do you already change your drum?pull out your developing unit and you can see cooper plate inside the machine,possibly its broken or this problem due to yourHV board.You can try change your AE sensor.
Very old model

SIMPLY Pull the developer section out.if u have loose toner then remove screws of the top cover of module .remove cover and pour it. if ur using a cartridge then align the cartridge face down with the module and pull the sleeve.thats it now u can't get a operational manual for such a old machine

Sounds as if the pressure spring that keeps the developer unit close to the drum is broken. Not worth fixing will cost around $250.

The new toner cartridge snap's into the top of the Hopper > just look on the box on how to install it. Once you have pulled the tab till you can read "STOP" push the slid back in and release the toner cartridge and you are done...... Put the empty cartridge into the "G" file

open the front cover, then you will need to slide out the piece the toner goes into, upper right side. Set the toner cartridge on top. You will see a tab to pull toward you, so the toner will drop down into the copier. Push the tab back in. Then push the cartridge toward the back of the copier a little and pull up.

In the same cartridge of toner new, this one the deposit of residues, the plastic shield moves back to empty the residual toner.

There is a door on the top of the copier to the right of the control panel (keyboard) which lifts open. The general instructions for adding toner is usually on the toner cartridge box and is fairly straight foreward. The toner cartridge is good for about 30,000 impressions.

wow that is hard to do i made the mistake doing that one time promised myself never to do that again took me quite a while to get it back in i dont know of any trick except persisitance just dont let the springs come off

The Unit where you've put the toner cartridge could be to far from the drum. Make sure your developer unit (unit where you've put the cartridge in) is locked in place.