Compatible Apple OS for iMac 3.6 GHz 10-Core Intel Core i9

If it is an iMac with an Intel Core i9, that narrows it down to

• iMac (Retina 5K, 27-inch, 2019)
• iMac (Retina 5K, 27-inch, 2020)

There were no 10-core CPUs in the 2019 models, so this iMac must be a 2020 one.

That Mac originally shipped with macOS 10.15.6 (Catalina), and you can upgrade it all the way to Sequoia. You almost certainly want one of the "most recent three" (Ventura, Sonoma, Sequoia).

How to download and install macOS - Apple Support

Upgrading a macOS depends upon the model Mac, specifications, and year. To get more information about your computer, choose:  (Apple menu) > 'About This Mac' in the upper left corner of any window, then "More Info..." or "System Report". There's more about this in "About System Information [Profiler] on your Mac" - System Information User Guide for Mac - Apple Support

Use the computer information, including the model year, and the links below to determine what is possible with your computer.

Click on this link to read how to get different versions of macOS --> How to download and install macOS - Apple Support

- The article also has links to system requirements for each OS version which you should check against your exact computer model. For any model produced in the last 5 years or so you should use the system requirements links for each OS version instead. This web site also has a reliable presentation of model and OS version compatibility: https://eshop.macsales.com/guides/Mac_OS_X_Compatibility

Please identify the exact year model of the iMac.

see > Identify your iMac model - Apple Support

Your 2020 iMac can run Sequoia: