how can I update from 10.13.4 to 10. 14. or newer

If you have a 2011 or earlier iMac you cannot go beyond 10.13.6. You will need to buy a newer Mac to run later versions of Mac OS. The reason being is because your 2011 (or earlier) simply does not have the hardware to support newer versions of Mac OS. Before you ask, no there are no work arounds and no your computer cannot have it's hardware upgraded. The ONLY solution is a new(er) Mac.

If you are unsure how to check the model year of your iMac please click the  in the upper left of the display and the click About this Mac and you will find the model year.

Back up your data, check your applications for compatibility, and depending on which iMac model you have, click on Mojave, Catalina, or Big Sur. It needs to be at least a 2012 one to run a newer OS.

(203247)

Welcome to the Apple Support Communities.

Please go to the Apple menu (top left) > About This Mac. What year is your Mac?

Jack