Can I install macOS 10.6.8 on a mid-2011 MacBook Air?
This really ends up build you asking yourself "What installer do you have to install 10.6.8?"

You can know the exact build and version of the potential installers and go through the documentation to see which models "support" that installer.


https://support.apple.com/en-us/HT201686


Furthermore, even if you don't have Apple official support, then you can see if you want to consider modifying the OS to hack it to try the install anyhow and see how badly it breaks. Lastly, some people use an installer to install from a supported machine to an external drive and then take that drive to the Mac that's not supported and see how badly things break when you boot. On iMacs, typical failure modes are WiFi not working and AirDrop / bonjour not working. Some of those items you can get around with USB adapters, other items you can't get around since the kernel and low level drivers are just not present to start up unsupported machines.


https://support.apple.com/en-us/HT201260
https://web.archive.org/web/20150225022618/http://support.apple.com:80/en-us/HT201260 (use archive.org to look at older versions of support articles)
https://web.archive.org/web/20150223074747/http://support.apple.com:80/en-us/ht1159


That last link shows all 2012 MacBook Air shipped originally with 10.7 so you would not expect 10.6 to have the drivers needed for full compatibility.