Need to update an old iMac running 13.6 to macOS Mojave 10.14 so I can restore my Time Machine backup from a MacBook Pro that is ailing. I have tried several combo updates, but they won't install without 10.14. I kept a backup on a USB drive, but

Does yor Mac qualify?

And avoid the combo Updates, only the full Installer is available from Apple, 11.04.6...

macOS Mojave 10.14.6 - Technical Specifications

General Requirements

OS X 10.8 or later

2GB of memory

12.5GB of available storage (OS X El Capitan 10.11.5 or later)*

Some features require an Apple ID; terms apply.

Some features require a compatible Internet service provider; fees may apply.

Mac Hardware Requirements

For details about your Mac model, click the Apple icon at the top left of your screen and choose About This Mac. These Mac models are compatible with macOS Mojave:

MacBook (Early 2015 or newer)

MacBook Air (Mid 2012 or newer)

MacBook Pro (Mid 2012 or newer)

Mac mini (Late 2012 or newer)

iMac (Late 2012 or newer)

iMac Pro (2017)

Mac Pro (Late 2013; Mid 2010 and Mid 2012 models with recommended Metal-capable graphics cards)

https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12

If you get a corrupted message...

Naw, it's not damaged, it's just that you have an old copy already in Applications, there are 2 cures...

Disconnect from the Internet & set the Date back to 2014, then you can run the Install MacsOS Mohave App in Applications, so expired Certificates are not expired.

Or... trash the Install MacsOS Mojave.app in Applications then a new copy can be downloaded.

How to get old versions of macOS  link will present the Full Version of Mojave 10.14.6

For Best results use Safari to commence the download as Others may not work.

Safari will open a redirect and open the Apple Store where the download can commence.

How old is the iMac?

13.6 is the last possible upgrade for late 2013 and earlier models.

The model year of an iMac is available at Apple menu > About This Mac.

I gave a link to it.