I am unable to update my Mac operating system. It is still on 13.6

camn21252 Said:

"I am unable to update my operating system on my iMac. It is still running 10.13.6"

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Verify Compatibility:

A. Start Here: Learn About Compatibility and how to Identify your Specific Mac Model - Apple Support

B. How to Verify:

I. Reveal your Model:

What is the Model of your Mac? To find out...

1. Go to: Apple menu
2. Click: About this Mac
3. View: Second Line-Down

then...

II. Compare the Results:

See if the Model you found is shown here:

• macOS Monterey is Compatible with these Computers - Apple Support
• macOS Big Sur 11 Hardware Requirements - Apple Support
• macOS Catalina 10.15 - Hardware Requirements - Apple Support
• macOS Mojave 10.14 - Hardware Requirements - Apple Support
• macOS High Sierra 10.13 - Hardware Requirements - Apple Support

III. If Compatible:

• Back Up your Mac First:  Be certain you Create a Time Machine Backup of your Mac, so that way you can have something to restore your Mac from, should anything go wrong with the reconfiguration.

The Age of this computer will Govern what newer version of macOS it will Qualify to install. Use About this Mac from the Apple Icon on Desktop - the required Information will be there.

With the above information in-hand - follow this How to get old versions of macOS and verify what version this computer Qualifies to install.  For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence

Caution - jumping over all the newer versions and directly to Monterey on Qualifying computers is Technically possible - there are those who have attempted and were successful. Then there are those who attempted and had less than good results.

If this is a Production or Mission Critical Set-up - a more prudent and measure approach is suggested. 

The above is from observations on the Apple Support Community Forums and IMHO

Tips Big Sir Upgrade Released Nov 2020

Tips Monterey Upgrade  Released Oct 25, 2021

Make Time Machine Backup  is very useful and can be used to Revert to Previous Working macOS

Notation - Mojave is the Last version to support 32 bit applications / extensions and Drivers. Catalina, Big Sur & Monterey supports only 64 bit and there is no workaround.

Suggest using Go64 to find 32 bit application before attempting the upGrade. Some or many of the Application already installed may required update or upGrades to 64 Bit Versions.

Are there any AntiVirus, Disk Cleaner, Optimizers, Un-installers, etc installed which should be removed as per Developers Instructions. They are useless, unneeded, cause havoc and interfere with the normal  operation of the OS and may even Corrupt the OS requiring a Reinstallation

Check if your computer is compatible with the next macOS upgrade. Here are the requirements for macOS Mojave 10.14: https://support.apple.com/kb/SP777?locale=en_GB