OP:
Be aware that to re-install using Mojave, you will have to COMPLETELY ERASE the internal drive on the iMac.
Not saying this to discourage you, but it WILL be necessary.
What I would suggest is:
- Download a copy of Mojave using the link MacManiac provided above. It should automatically be downloaded into your applications folder
- Get a USB3 flashdrive 16gb
- Get the free app, "Diskmaker X" from here:
diskmakerx.com
- Use Diskmaker to create a bootable USB flashdrive installer
- Now, boot from the flashdrive (hold down option key continuously at startup, select installer from startup manager)
- DO NOT run the installer yet. Instead, quit the installer and open Disk Utility
- Go to the view menu and choose "show all devices"
- Select the topmost item (on the left) that represents the internal drive
- ERASE it to APFS, GUID partition format
- Quit Disk Utility
- Reopen the OS installer and let it do its thing
- When done be ready to migrate your data during the initial setup process. I recommend that you use an external drive as "an intermediary" for your data, and I also recommend that it be a cloned backup using either CarbonCopyCloner or SuperDuper. But this is the topic of another discussion...