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I just purchased a used Apple Mac Mini A1347 Desktop - MGEM2LL/A (Late 2014) to run software which can’t be used with a system newer than macOS Mojave 10.14.6.
This Mac Mini came with macOS Catalina 10.15.7 installed.
I’ve downloaded macOS Mojave 10.14.6 ‘UPDATE’ from the net, but it won’t install.
Is it because it’s an update?
You must erase the drive before you can downgrade the macOS to a previous version.
You can reinstall a previous macOS version by restarting the Mac in recovery mode. Then after, you can apply the upgrade to Mojave if necessary.
Boot your Mac in Recovery mode by restarting and when you hear the startup chime press the Command-R (⌘R) keys until you see the Apple logo and progress bar. Use a wired USB keyboard for this. When the macOS Utilities window appears, select Disk Utility.
Click Disk Utility > View > Show All Devices, then select the top-most drive device on the left.
Click Erase and then set the parameters:
use GUID partition map scheme. Click erase to complete the process.
Please see > How to reinstall macOS from macOS Recovery - Apple Support
Also see > How to create a bootable installer for macOS - Apple Support
And, since we don't know where you downloaded your Mojave installer and I suspect it's an updater rather than the full installer, I recommend you delete the one you have and download a new installer from the link in this document > How to get old versions of macOS - Apple Support
You must erase the drive before you can downgrade the macOS to a previous version.
You can reinstall a previous macOS version by restarting the Mac in recovery mode. Then after, you can apply the upgrade to Mojave if necessary.
Boot your Mac in Recovery mode by restarting and when you hear the startup chime press the Command-R (⌘R) keys until you see the Apple logo and progress bar. Use a wired USB keyboard for this. When the macOS Utilities window appears, select Disk Utility.
Click Disk Utility > View > Show All Devices, then select the top-most drive device on the left.
Click Erase and then set the parameters:
use GUID partition map scheme. Click erase to complete the process.
Please see > How to reinstall macOS from macOS Recovery - Apple Support
Also see > How to create a bootable installer for macOS - Apple Support
And, since we don't know where you downloaded your Mojave installer and I suspect it's an updater rather than the full installer, I recommend you delete the one you have and download a new installer from the link in this document > How to get old versions of macOS - Apple Support
Just to add...
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)
Don't use FireFox for these links…
https://itunes.apple.com/us/app/macos-mojave/id1398502828?mt=12
Problems installing macOS Mojave 10.14.6
