SecureErase (Category 4 - DoE 3 - Pass Secure Erase) Macintosh HD - in Terminal app

It is also possible the hard drive for a 2012 computer is worn out and failing which is why it may be taking longer to complete each pass.

If you just want to perform a secure erase and don't require multiple passes, then how about booting from a Knoppix LInux USB stick and utilizing the hard drive's built-in hardware secure erase feature? For a hard drive, this built-in hardware secure erase feature does nothing more than write zeroes to the entire drive, but it may perform a bit faster than manually writing zeroes to the drive through software. This is also the best way to securely erase an SSD without causing undue wear to the SSD, plus it may fix some SSD issues since an SSD's built-in hardware secure erase feature also resets an SSD to factory defaults.

https://ata.wiki.kernel.org/index.php/ATA_Secure_Erase

Of course @John Galt's suggestion for encrypting the drive first followed by a simple erase is problem the best & easiest option for most people. Keep in mind that Apple is removing features from macOS with the secure erase feature being one of them which was removed from the Disk Utility GUI since it would wear out SSDs, but the feature still remains within the command line version of "diskutil" although I have never used it.

I won't dissuade you from using Terminal if you wish. Considering your goal is assured data destruction, you won't be risking anything.

The Shift-Option-Command-R startup key chord will allow you to use the version of Terminal that came with that Mac back in 2012, considering subsequent versions of diskutil have eliminated certain options.

man diskutil and scroll to the end for its (recent) history.

I would be remiss if I did not point out the NOTE in its description of secureErase — not that it applies in your case, since your concern is magnetic media. I point it out only for readers who may run across this Discussion years from now, when hard disk drives are relegated to the ash heap of computing history... where they belong.

And, yes, I could just remove the hard drive and hammer it into oblivion, but that's not what I wish to do.

I prefer a similar technique, performed at a safe distance.

No, you assume wrong. I’ve replaced the hard drive in my 27” iMac twice, replaced the DVD/CD drive with an SSD, added a custom SATA cable with a temperature sensor, upgraded RAM to 32GB and removed the SSD and disk before retiring my 9 year and 9 month old iMac. 

You could also put the iMac into target disk mode, and if you have the right cables and the other system will accept those cables, you could do all this without taking the drive out of the iMac.

I will move forward with finding someone who can guide me through a level 4 Secure Erase procedure.

Did you try booting the Internet version of macOS Recovery as I explained?

John Galt wrote:

The Shift-Option-Command-R startup key chord will allow you to use the version of Terminal that came with that Mac back in 2012, considering subsequent versions of diskutil have eliminated certain options.

That version of diskutil might permit the secureErase 4 option you seek to accomplish.

The obvious error in your initial attempt to use that command is that a space character is required after the option 4. That is at least one reason Terminal objected to the command as entered.

In other words,

diskutil secureErase 4 /Volumes/Macintosh\ HD

There may be other reasons for its objection but see if the above gets you any closer to what you want.

I no longer use any Macs that incorporate internal hard disk drives. That limits my ability to help but I might be able to cobble something together if need be.

SteveHS wrote:

"...never use these options for an SSD as SSDs don't work the same way as hard drives".

In that case, I've come to a dead-end.

Wait a minute — are you saying the storage device you are attempting to "secure erase" is a SSD and not a hard disk???

SteveHS wrote:

Thank you, John.

I tried your suggestion of adding the space after the number 4 : diskutil secureErase 4 /Volumes/Macintosh\ HD

That resulted in the following statement: "Could not find the disk hd".

I think you may have made a mistake typing the command by omitting the backslash after "Macintosh" in the path even though you are showing it in your post. The backslash is critical for the correct path in order to include the space in the path. Instead of using the backslash in the path to "escape" the space, you can include the path within double-quotes instead. Either of the two following commands are equivalent and should work:

diskutil  secureErase  4  /Volumes/Macintosh\ HD

diskutil  secureErase  4  "/Volumes/Macintosh HD"

(Please note - this procedure WAS NOT carried out in RECOVERY MODE)

Was it carried out while booted from a macOS USB installer? Or while the Mac was in Target Disk Mode connected to another Mac? Or an external full macOS boot drive? Otherwise, you cannot erase the drive you are booted from.