Does Zorin support this printer and its scanner? What's the best way to install it?
You can download the driver from hp site:
https://support.hp.com/ch-de/drivers/samsung-scx-3400-laser-multifunction-printer-series/17156995
Select Linux as OS and Ubuntu. Then download the tar.gz file and unzip it.
I'm not sure if it will work on Zorin/Ubuntu 24 because it is an older driver.
When the unzipped package is a normal .deb file, you can doubleclick on it and you are asked if you want to install that file. If that doesn't happen and the folder is opened, then right-click on an empty space and select "open terminal here".
Then enter in terminal
sudo ./install.sh
After the installation click on your Zorin start menu and search for the app.
You can start Zorin in Live Mode from the USB Stick and check this Way if Your Printer is detected.