Can I update my iMac running macOS Sierra 10.12.6?

Yes. If your iMac is currently running macOS 10.12 Sierra, you can at least upgrade to macOS 10.13.6 High Sierra.

If your iMac is a Late-2011 model or newer, then you have additional upgrade options.

If it is much newer, then your options multiply - maybe even up to macOS Ventura, depending on the model year of the computer.

• macOS 10.13 High Sierra is compatible with the Macs listed here (c.2009)

• macOS 10.14 Mojave is compatible with the Macs listed here (c.2012)

• macOS 10.15 Catalina is compatible with the Macs listed here (c.2012)

• macOS 11 Big Sur is compatible with the Macs listed here (c.2013)

• macOS 12 Monterey is compatible with the Macs listed here (c.2015)

• macOS 13 Ventura is compatible with the Macs listed here (c.2017)

Please note that upgrading to macOS 10.15 Catalina or newer will require that you also update/upgrade or find replacements for any older 32-bit applications. You can use this free utility to check the compatibility of your apps:

St. Claire Software – Go64: https://www.stclairsoft.com/Go64/

Also, I suggest that if your iMac is a 2015 model or older then you may upgrade the machine, but you should be considering very seriously replacing the old obsolete iMac. It will not run any of the three most recent and still supported macOS versions. The support situation will not improve for that iMac.

Any iMac that can run Sierra (10.12.*) can be updated at least to High Sierra (10.13.*).

If your iMac has a hardware model year of 2012 or later, you can update to Catalina (10.15.*), and possibly beyond. Catalina breaks 32-bit applications but is recent enough to run current versions of Firefox, LibreOffice, GIMP, and the commercial Affinity V2 programs (Photo, Designer, Publisher).

Best case scenario would be an iMac with a hardware model year of 2017. Those can run Ventura. (If your iMac is running Sierra now, it is too old to be compatible with Sonoma, Sequoia, or the not-yet-released Tahoe.)

What does it say about your Mac's hardware model year in  > About This Mac?

what you can update to depend on the model if imac you have

Identify your iMac model - Apple Support