Can I update to 10.12 or higher on my late 2012 iMac?

A late 2012 iMac can be upgraded to Catalina 10.15.7 but no later. See: How to get old versions of macOS - Apple Support

Also, if you have any non Apple 32 bit apps installed they will also need to be upgraded if you upgraded to Catalina. See: https://www.macworld.com/article/232735/how-to-check-if-mac-software-is-32-or-64-bit.html

A 2012 iMac can run up to macOS 10.15 Catalina.

However, if you have older apps like Office 2011 or older, or old version of Adobe Creative Suite, they will not run under Catalina; you will have yo buy newer versions of most.

What OS does the apps in question require? To avoid the Catalina compatibility problem you can update to Mojave which mostly still supports older apps.

Links to nstallers for older versions of macOS are available in this Apple support document:

How to get old versions of macOS - Apple Support

The situation with older v. newer apps is laid out in this article:

32-bit app compatibility with macOS High Sierra 10.13.4 and later - Apple Support