How to fix E: Unable to correct problems, you have held broken packages (multiarch) in APT

First, identify your system architecture and see if multiarch is enabled:

dpkg --print-architecture
dpkg --print-foreign-architectures

This shows your primary architecture (usually amd64) and any foreign architectures (like i386) you have enabled.

List all packages currently held by the system:

sudo apt-mark showhold

This displays which packages are preventing apt from making automatic changes. Note any packages related to the multiarch installation you attempted.

Refresh your package lists and check for broken packages:

sudo apt update
sudo apt check

The apt check command will report any dependency issues in your system.

Release the hold on packages that are causing the conflict. Replace "package-name" with the actual package name:

sudo apt-mark unhold package-name

If you need to unhold multiple packages, repeat this command for each one. You can also unhold all packages at once:

sudo apt-mark unhold $(apt-mark showhold)

Use apt install with the fix-broken flag to attempt automatic dependency resolution:

sudo apt install --fix-broken

This command will try to resolve unmet dependencies by installing missing packages or adjusting package versions.

If apt still cannot resolve the conflicts, try aptitude, which has a more sophisticated dependency resolver:

sudo aptitude install package-name:arch

When aptitude encounters conflicts, it will suggest alternative solutions. You can also use:

sudo aptitude why-not package-name

to understand why a package cannot be installed.

If dependency resolution fails, remove the problematic package and try again:

sudo apt remove --purge package-name:arch
sudo apt autoremove
sudo apt update

Then attempt to install a compatible version or remove the multiarch requirement.