Broken Package Manager? The suggested "apt-get -f install" is failing!

Usually this happens when mismatched package versions are hand-installed with dpkg or gdebi without some of the dependencies having a resolution. (dpkg/gdebi and other .deb level tools will try to install a package where dependencies are unmet, leaving it in the half-installed "unconfigured" state, which apt considers to be broken. apt, software center, synaptic, and other high-level package management will usually catch these errors from reading the dependencies before installing the package and stop you before you break things, unless the error happens late in the installation, such as what happens when a package in the repository is broken and tries to write files owned by another package)

So long as the packages causing the error are not system critical and can be removed without causing a huge cascade of dependency problems, the quickest way to resolve an error like that that apt-get can't resolve on it's own is to back the offending packages out until apt-get -f install is able to take care of the problem, then apt-get update, apt-get upgrade, and finally try what you were doing again through apt-get.

In your case, I'd start by backing out libcupsimage2:i386 ia32-libs-multiarch:i386 and skype:

apt-get remove libcupsimage2:i386  ia32-libs-multiarch:i386 ia32-libs skype

If the situation is more complex, and creates huge cascades of failed dependencies, then the alternative is to figure out from the dependency messages what went wrong and try to specify a solution by naming the packages necessary to resolve the dependency problem. Usually these sort of situations arise from mixing packages from multiple repositories such as backports or PPAs, and you solve them by specifying a particular version of a package that wouldn't normally be considered by apt because of pinning, or by explicitly telling apt-get to go back to versions in the official repository (apt-get will not downgrade a package to solve a broken situation unless explicitly told to do so - so if you installed a newer version of a library by hand, and packages on the system have a dependency on the specific version, you have to update one or downgrade the other until the dependency mess is resolved.)

To remove the mismatched Package or half installed package that creates problem with dependencies. Try

sudo apt-get autoremove

This will remove mismatched package. After that, you will able to reinstall package.