Packages, broken or otherwise makes me think of the post office or a courier service.
Linux uses packages every day, whether you like it or not. When you install or remove a program packages are either downloaded or removed. Debian uses .deb files (Peppermint Linux is a decendant of Debian, Ubuntu and Mint).
Recently, there was a widespread problem with Peppermint Linux. Peppermint uses the Mint update manager, and this keeps the system up to date with new updates. However, Mint update did not want to update and gave an error saying "Broken Packages", and asking you to fix the problem before you can update further.
Now, as far as I can tell, Mint Update will download new updates EXCEPT if the update is a RISKY update. Then it tries to update the other packages, and if one of the packages that needs to be updates DEPENDS on the other RISKY package (too risky to be updated by Mint Update), so then you get a broken packages error.
There is a work around, or fix for this. The packages in question are VLC files, so you need to open Synaptic Package Manager, then type in VLC and update the installed VLC packages.
After that, open a Terminal window and type in:
This should fix the problem and you can once again have an up-to-date Peppermint Linux system.