Sorry to resurrect this thread, I had to go through this recently so wanted to share my experience for anyone out there who may need to do the same. I won’t go into reasons for doing this, suffice to say sometimes you have to run a studio or lab using equipment that’s just not compatible with newer hardware or OS and is either prohibitively expensive or simply impossible to replace. That being said the iMac I worked won’t be connected to internet, and I would never recommend connecting an older machine that’s not patchable to the web. And yes it's very possible even in 2021 to perform the downgrade, although it's probably not for the feint of heart. This was done on a mid-2011 12,2 iMac.
Step 1, find the install media and make a bootable USB image
You might be able to borrow install media, buy it or find it on the internet, each has its own caveats. A popular archive org site maybe helpful in researching a 10.6.7 iso image. Downloading an image from wild has its own risks so it's preferable to locate the original DVD image.
To make bootable USB, I followed similar steps to here, essentially using Restore function within Disk utility
https://business.tutsplus.com/tutor...e-usb-drive-with-os-x-snow-leopard--cms-21491
For whatever reason this only worked on 10.13 and not on my more up to date mac.
Step 2, ensure install media will work with your mac
Back in the day Apple used to match install media (DVDs) to the type of Mac. So if you obtained an image that’s for a macbook pro and made a USB install media, it likely won’t work on an iMac. There are many tutorials out there to help with this problem (OSinstall.mpkg), even a very popular retro computing YouTuber The 8-bit Guy has a video that may be helpful.
Steps 1&2 really worked better on older versions of MacOS (10.13, 10.11) probably due to security restrictions on 10.15. There is probably a way around it, I just found it easier to try on an older mac and discover that it just worked.
Step 3, erase 10.13 completely from the iMac (including restore partitions)
The 10.6.7 installer doesn’t like the restore partition from 10.13 that would persist even after you format the drive using disk utility before you start the install. You can easily make a bootable USB GParted image and use it to remove ALL (efi, restore, main) partitions from all the hard drives and format them with HFS+ format.
https://gparted.org/liveusb.php
Step 4, Install 10.6.7 and upgrade
Boot the iMac using the USB image made in steps 1&2 and use disk utility to format the drive yet again and then proceeded to install. Update the system to 10.6.8.
I hope I’m not causing trouble posting this information here. These iMacs are still incredibly capable machines and they have no problem running older equipment that would likely land up in a landfill without the capability to run on older versions of OS. Good luck!