"Can someone step me through how to take 10.12.4 off my good iMac; burn it to disc for example? Or does the installer have things on it that my machine does not have?"
You will need an external drive of sufficient capacity.
You will need either CarbonCopyCloner or SuperDuper.
Both of these are FREE to download and use for the first 30 days -- long enough to do what you need.
Connect the external drive to the iMac.
Open Disk Utility and erase it, to HFS+ with journaling enabled.
Now, launch CCC.
Put your source drive (iMac internal drive) on the left in CCC's window.
Put your target (external drive) to the right of the source drive.
You can accept CCC's defaults for this clone.
Then... let 'er go.
CCC will ask if you wish to clone the recovery partition, I'd suggest that you do this too.
Take the cloned backup to the "new" iMac and connect it.
Boot the iMac, but hold down the option key and KEEP HOLDING IT DOWN until the startup manager appears.
Select the external drive with the pointer and hit ok
The [new] iMac should now boot from the external drive.
When you get to the finder, go to "about this mac" (Apple menu) and verify that you are booted from the clone (it should look just like your OLD iMac).
Now you can do this:
Use Disk Utility to ERASE the contents of the internal drive on the new iMac, then...
Launch CCC again, and RE-CLONE the contents of the backup drive to the internal drive on the new iMac.
When done, you should be able to boot the new iMac.
Again, reboot with the option key held down for the startup manager.
Select the internal drive and hit return.
It will boot and look exactly like the old one.
TIP: Open system preferences, go to "startup disk", and set the internal drive as the boot volume (this is required because you replaced the contents of the internal drive).
WARNING!
This will erase anything that is currently on the new iMac's internal drive, so you have to save anything you want from it BEFORE you do the above procedure.
Print out these instructions for reference.
