Hi asphalt_angel,
I understand you have an Officejet Pro 8600 Premium that is not recognizing the new HP cartridges you're trying to insert. I'm sorry to hear this has been happening but I will certainly do my best to assist you with this issue.
Since I'm not sure what the exact error is that you're getting, I would recommend first that you follow this An 'Ink Cartridge Failure,' 'Incompatible Ink Cartridges,' or 'Ink Cartridge Problem' Error Message Displays on the All-in-One document as it covers most cartridge errors that you would see. If the issue persists after trying those steps, please remove all 4 cartridges from the printer, and then perform a hard reset. Once the printer is starting back up and tells you to insert the cartridges, insert them one at a time and close the door after each one to make sure the printer recognizes it.
Hope this helps, have a great day!!