I have High Sierra 10.13 on iMac I tried to update to Ventura, Monterey, Big Sur, Mojave but I get a message saying

chiman119 Said:

"I have High Sierra 10.13 on iMac I tried to update to Ventura, Monterey, Big Sur, Mojave but I get a message saying: 'We could not complete your Purchase. This version of macOS10.14.6 cannot be installed on this computer'"

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Troubleshooting macOS Update:

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 Ventura is Compatible with these Computers - Apple Support
• 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

then...

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.

It sounds like your iMac is not compatible with (i.e. too old) to install Mojave or later.

Exactly what model iMac do you have? Look in About This Mac and tell us what it says.