Even if you don't know the broken package name, synaptic does and will repair the install: it is a dependency hence the other part of the message (will not be installed..)https://help.ubuntu.com/community/SynapticHowto
How to fix broken packages
'Broken packages' are packages that have unsatisfied dependencies. If broken packages are detected, Synaptic will not allow any further changes to the system until all broken packages have been fixed.
1.To fix broken packages
1.Choose Edit > Fix Broken Packages from the menu.
2.Choose Apply Marked Changes from the Edit menu or press Ctrl + P.
3.Confirm the summary of changes and click Apply.
If that does not help, then please follow this procedure:
https://help.ubuntu.com/community/Packa ... gProcedure
You can always look at mint's own package manager (I don't like it much either --find it has too much non-user control, I always use synaptic or apt on the terminal )
--and see if wine is there and which version: if it is lower than the version you want, you will just have to use source files and include any dependencies needed, and even then it may be a long haul to make it work. You need to fix each item that causes any error..