I'm running High Sierra 10.13.6 can I download Mojave 10.14.6 or Catalina 10.15.

This lists the requirements for High Sierra.

How to upgrade to macOS High Sierra – Apple Support

And this for Mojave:

How to upgrade to macOS Mojave – Apple Support

MacBook introduced in 2015 or later

MacBook Air introduced in 2012 or later

MacBook Pro introduced in 2012 or later

Mac mini introduced in 2012 or later

iMac introduced in 2012 or later

iMac Pro (all models)

Mac Pro introduced in 2013, plus mid-2010 or mid-2012 models with a recommended Metal-capable graphics card.

If your iMac is a 2012 or newer model, yes. Otherwise, no.

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