Is MacOS X compatible with Mac Monterey?

There were many versions called Mac OS X, before it was renamed OS X, before it was renamed macOS. macOS is the current name for the same operating system.

The 2 biggest issues for 3rd party vendor software are

A) if the software is compiled for 32-bits it will Not run on anything beyond macOS Mojave 10.14. Monterey is macOS 12.0

B) if the software required the installation of kernel extensions (very few apps did this). If it did require kernel extensions, then it could get caught in the 32-bit situation, or it could be caught because macOS, starting with Catalina 10.15, and in Big Sur 11.0, Apple stopped allowing many 3rd party kernel extensions.

If your app is compiled for 64-bits, then there is a good chance it will still run on Monterey.

It would be best to check with your software's vendor to see if your current version will run, or if there is an upgraded version that will run on Monterey.

Monterey is a version of macOS (Mac OS X). Version 12 to be specific.

If software requires macOS or even Mac OS X, then it may run. It depends on what version Mac OS X is required.

What exact software are you trying to run?

And what, exactly, does that software say that is required to run it?

Please be specific, it's important.