how do I update my mac mini from osx10x10 to 10.11 or later?

Depending on your exact model of Mac mini will be what macOS version you can update to.

Go to Apple Menu->About This Mac, and post back with model year.

In the meantime, you can see here for how to update to the current macOS 11.3 Big Sur (if supported): link-> How to upgrade to macOS Big Sur - Apple Support

Or here to get older versions of macOS: link-> How to get old versions of macOS - Apple Support

Niel wrote:

Back up your data, check your applications for compatibility, and click on El Capitan, High Sierra, Mojave, or Catalina.

Phil0124: The model year is in the original message.

(198252)

Ahh, so it is. Not sure how I missed that. Thanks.

In that case, it can update to 10.15 Catalina, but not macOS 11 Big Sur.

Back up your data, check your applications for compatibility, and click on El Capitan, High Sierra, Mojave, or Catalina.

Phil0124: The model year is in the original message.

(198252)