Can I upgrade my iMac from High Sierra to Monterey?

You can upgrade to Mojave (10.14.*) or Catalina (10.15.*). For that iMac, Catalina is the end of the line.

If you upgrade to Catalina,

• 32-bit applications will stop working
• iTunes will go away, replaced by separate apps: What happened to iTunes? - Apple Support

these are the computer which support montery

macOS Monterey is compatible with these computers - Apple Support

Your choices are...

macOS Mojave 10.14.6 - Technical Specifications

General Requirements

OS X 10.8 or later

2GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible Internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Mojave:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with recommended Metal-capable graphics cards)

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

macOS Mojave - Technical Specifications

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

macOS Catalina - Technical Specifications

General Requirements

• OS X 10.9 or later
• 4GB of memory
• 12.5GB of available storage (OS X El Capitan 10.11.5 or later)*
• Some features require an Apple ID; terms apply.
• Some features require a compatible internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Catalina:

• MacBook (Early 2015 or newer)
• MacBook Air (Mid 2012 or newer)
• MacBook Pro (Mid 2012 or newer)
• Mac mini (Late 2012 or newer)
• iMac (Late 2012 or newer)
• iMac Pro (2017)
• Mac Pro (Late 2013 or newer)

How to download and install macOS - Apple Support

https://apps.apple.com/gb/app/macos-catalina/id1466841314?ls=1&mt=12

In case you're running into issues with your version of Safari being too old …

If you upgrade to Catalina, you can run the current version of Firefox:

https://www.mozilla.org/en-US/firefox/new/

If you remain on High Sierra, or upgrade to Mojave, you can run Firefox 115 ESR. It isn't getting new features any more, but Mozilla says they will provide "critical security updates" for it until September 2024.

https://support.mozilla.org/en-US/kb/firefox-users-macos-1012-1013-1014-moving-to-extended-support