I have an Imac with macOS High Serra 10.13.06. It's about 6 years old. Can macOS Catalina be installed on it?

All iMacs that are 2012 and later models can have Catalina installed. You can verify what year your Mac is from by clicking the Apple symbol in the upper left the display and then click About this Mac it will look similar to my screen shot below where you will see mine is a 2011 model:

Go to Apple > About This Mac and tell us exactly what year model your iMac is.

see > Identify your iMac model - Apple Support

If your iMac is a late 2012 model or newer it and run Catalina.