Imac late 2012 27" Macintosh accidentally deleted

Install El Capitan or Later from Scratch

If possible, back up your files.

1. Restart the computer. Immediately, at or before the chime, hold down the Command and R keys until the Apple logo and progress bar appear. Wait until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu and click on the Continue button.
3. When Disk Utility loads select the target drive (out-dented entry w/type and size info) from the Device list.
4. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
5. Set the partition scheme to GUID.
6. Set the Format type to APFS (SSDs only) or Mac OS Extended (Journaled.)
7. Change the disk name to "Macintosh HD" without the quotes.
8. Click on the Apply button, then wait for the Done button to activate and click on it.
9. Quit Disk Utility and return to the Utility Menu.
10. Select Install OS X and click on the Continue button.

This should install the version of macOS last installed on the computer.

If you no longer have a working Recovery HD, then you will have to do the following instead:

Internet/Network Recovery of El Capitan or Later on a Clean Disk

     If possible back up your files before proceeding.

1. Restart the computer. Immediately, at or before the chime, hold down the (Command-Option-R) keys until a globe appears.
2. The Utility Menu will appear in from 5-20 minutes. Be patient.
3. Select Disk Utility and click on the Continue button.
4. When Disk Utility loads select the target drive (out-dented entry w/type and size) from the side list.
5. Click on the Erase button in Disk Utility's toolbar. A panel will drop down.
6. Set the partition scheme to GUID.
7. Set the Format type to APFS (SSDs, only if installing Mojave or Catalina ) or Mac OS Extended, (Journaled.)
8. Change the disk name to "Macintosh HD" without the quotes.
9. Click on the Apply button, then click on the Done button when it activates.
10. Quit Disk Utility and return to the Utility Menu.
11. Select Install OS X and click on the Continue button.

You will need an active Internet connection, Wi-Fi or Ethernet. The latter is preferable.