External disks don't shown iMac

"don't show"? where?

On your desktop? check your Finder preferences to see if you have External Disks hidden.

In Disk Utility.app? Your machine doesn't recognize/detect the drive - check your cables and connections. If they look good, try connecting the drive to a different machine (if you have one). If that fails the drive has likely failed.

It also helps to know the exact model of your iMac and version of macOS being used. You can get this information by clicking the Apple menu and selecting "About This Mac".

Also, what are the exact make & model of the external drives?

Make sure to try connecting the drives directly to the iMac and disconnecting all other external devices in case one of them is causing a problem. An adapter or cable can also sometimes be a problem as can docks & hubs.

Edit: And what file system is being used on the external drives? Are you using any third party software to manage the external drives?

Try booting into Safe Mode to see whether you can access the external drives.

Do they show in Disk Utility?

1.. Shut the machine down.

2.. UNPLUG the power lead to the computer and any peripheral devices.

3.. leave it for 10 minutes.

4.. Hold power Button in for 10 seconds

5.. Connect everything back up and restart.