I just purchased the New Mac Mini 2018

The computer will refuse to install it. You can only install the OS version or higher that came with the computer. Even if you could install it, the computer would show boot errors. The disc itself might also refuse to install, if it is a disc that came with another model computer originally.

You can't just stick in a Snow Leopard DVD and install it. The hardware will reject it because Snow Leopard has no idea how to run a computer built for Mojave, then too the disc itself may reject the hardware it it came for use with a different computer (and then this gets into the whole licensing issue and talk about Snow Leopard Server, as we still have no idea which version of Snow Leopard you have)). You have to run software such as VirtualBox to emulate (pretend) a different kind of machine -- a vm = Virtual machine - Wikipedia

I have no experience with setting this up but it seems other have done it at least with Sierra: virtualbox.org • View topic - [Solved] Snow Leopard guest, Sierra host on new (late 2016) MBP

I'll let you peruse the VB forums to see if you can find newer. Realize this is not likely to be a 5 minute job, particularly if you are running macOS that is relatively new and the people writing things such as VB are still working out their end of the software.

Only by running Mac OS X 10.6 Server through a product such as VirtualBox.

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You can get Parallels Lite from the MacApp Store and you will be

able to install any macOS in its virtual environment free of charge.

It will likely be less troublesome to get working than Virtual Box.

you may have to verify that virtualbox support running macOS vm's at least on windows it's difficult because macOS is legally only allowed to run on macs

parallels the commercial vm support it though maybe because they are macOS only

Snow Leopard Server is a special version of Snow Leopard which is no longer available through Apple (at least when I bought one 3 years ago they had to spend 10 minutes hunting for a copy while I was on hold on the phone, so I got the impression I got one of the last copies).

That's not Snow Leopard at all, it is Leopard. According to the post I linked earlier you would also need the server version of Leopard for Parallels to work. It will say "server edition" or something similar on the box (I have one). If it is a grey disc it is one that came with a computer and is not a server edition. If it is a regular retail upgrade disc it also won't say server.

We still don't know which exact Snow Leopard disc you have and unless you have a server version disc (very unlikely unless you specifically purchased one from Apple), Parallels may not work.

KB Parallels: Unable to install Mac OS (Snow) Leopard as a guest OS