Can you install straight from OS X 10.8 Mountain Lion to macOS 10.15 Catalina on a Mac?

Before upgrading make a full back up of your Mac.

Check that third party apps you use have updates available for the new OS.

https://roaringapps.com

Check that your printers/ scanners etc have updated drivers and software available for the new OS.

macOS Catalina 10.15 was released recently, the latest version of macOS.

If you are considering upgrading to Catalina be warned that it does not support 32bit apps.

Your Mac is probably running 32bit apps and these will need to be updated to 64bit apps,

some updates may be free, some may be paid. Use this app to discover which apps you have

are 32bit, https://www.stclairsoft.com/Go64/. Once the list has been created you can then

contact the developers of the apps to see if they provide 64bit updates. 

How to upgrade to macOS Catalina – Apple Support

Be prepared for BIG changes and Santa will not be able to sort you out.

Why not? If the mac allows for Catalina, it should work. I'd trust the system-updater, if it tells that you have a go, then go.

(Since mountain lion is quite some time ago, your hardware may not be suited for Catalina. The updater will tell you. It won't tell you wether it'll run smooth though)

hth

david