Can I update from Mojave to Monterey?

If your iMac is a late 2015 or later model, see: How to upgrade to macOS Monterey - Apple Support

If not, see the following:

The model year of an iMac is available at Apple menu > About This Mac.

An early 2009 iMac can be upgraded to El Capitan 10.11.6 but no later version. See: https://support.apple.com/en-us/HT211683

A late 2009 through mid 2011 iMac can be upgraded to High Sierra 10.13.6 but no later version. See: https://support.apple.com/en-us/HT211683

A late 2012 through late 2013 iMac can be upgraded to Catalina 10.15.7 but no later. See: https://support.apple.com/en-us/HT211683

A mid 2014 and late 2014 can be upgraded to the latest version of Big Sur macOS 11 but no later. See: https://support.apple.com/en-us/HT211683

A late 2015 or later can be upgraded to the current version of Monterey macOS 12. See: https://support.apple.com/en-us/HT212735

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.

Does the >>  Computer Qualify for the Monterey upgrade 

macOS Big Sur 11 hardware requirements

macOS Catalina 10.15 hardware requirements

macOS Mojave 10.14 hardware requirements

Caution - jumping over all the newer versions and directly to Big Sur  / 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