I have mac OS High Sierra 10.13.6 on my computer now. Can it be updated to to a higher version?

if this is an iMac 21.5” from late 2012 or newer, yes.

See 🍎 > About This Mac for that info.

Late 2012 and newer can be updated to at least Mojave, and potentially more recent.

Full details: How to get old versions of macOS - Apple Support

Have a backup prior to any upgrade.

If upgrading to macOS Catalina or newer—past Mojave—all of your apps and all printer and scanner drivers must all be 64-bit apps. You can use the tool Go64 to find existing 32-bit apps that will need to be updated, replaced, or retired. This includes upgrading or replacing Microsoft Office 2012 and earlier, if you are using that suite.

Back up your data, check your applications for compatibility, click here, and depending on which iMac model you have, then on the download link for Mojave, Catalina, Big Sur, or Monterey; it needs to be at least a 2012 one to run a higher OS. If you get a Mac App Store preview page, change the https at the beginning of its address to macappstore.

Catalina and newer won't run 32-bit software; download and use Go64 to scan for it. To look other programs up, click here.

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2old2getit wrote:

Great! It’s says iMac (21.5-inch, Late 2021)

How do I update it?

Check that iMac.

iMac is 24” model and not 21.5”, with M1, for the 2021 models, and cannot run High Sierra.

If you have iMac 21.5” Late 2011, that model cannot be upgraded past High Sierra.

Full details on upgrades (also links to Monterey): How to get old versions of macOS - Apple Support

Have a backup prior to any upgrade.

If upgrading to macOS Catalina or newer—past Mojave—all of your apps and all printer and scanner drivers must all be 64-bit apps. You can use the tool Go64 to find existing 32-bit apps that will need to be updated, replaced, or retired. This includes upgrading or replacing Microsoft Office 2012 and earlier, if you are using that