Install older OS X on latest Mac Mini
You can not install older OS X versions on newer models, the old OS X version are missing the required drivers for hardware not even available when the OS X version was released.

I see several options:


You may (legally) install 10.6.8 Server in a VM (Parallels or VMware) though. 
The latest MacMini supporting 10.6.8 is the MacMini4,1: Apple Mac mini "Core 2 Duo" 2.4, Apple Mac mini "Core 2 Duo" 2.66 &amp; Apple Mac mini "Core 2 Duo" 2.66 (Server)
With some workarounds and hazzle you will get 10.6.8 working on MacMini5,1 and MacMini5,2. In the comments there (March 12, 2013 Gregg Tomlinson) even a working MacMini6,1 is mentioned:


  I believe it does – I am using this on a 2012 MacMini that came with Snow Leopard [sic!], and reverse-engineered it to use 10.6 with this methodology.