what is the newest OS i can install on my imac, late 2015 which now has High Sierra 10.13.6

Monterey…

macOS Monterey is compatible with these computers - Apple Support

• iMac – all models from late 2015, iMac 16,1 – 20,2
• iMac Pro – all models, iMac Pro 1,1
• MacBook & MacBook Retina – all models from early 2016, MacBook 9,1 – 10,1
• MacBook Pro – all models from early 2015, MacBook Pro 12,1 – 17,1
• MacBookAir – all models from early 2015, MacBook Air 7,1 – 10,1
• Mac Mini – all models from 2014, Mac Mini 7,1 – 9,1
• Mac Pro – all models from 2013, Mac Pro 6,1 – 7,1

https://wpbeaches.com/apple-minimum-system-requirements-for-macos-monterey-12/

https://apps.apple.com/us/app/macos-monterey/id1576738294

macOS Monterey on the App Store (apple.com)

https://apps.apple.com/us/app/macos-monterey/id1576738294?mt=12

A late 2015 iMac can run up to Monterey which is what I use and would recommend.