Well there's a few different ways to do it. One way would be with a dual(or 2)pole, multi throw switch like a DPDT (2pole 2throw). The number of poles is how many separate "switches" are operated by a single switch. You want dual pole (or quad if you're doing balanced) because stereo is 2 channels therefore with each switch you use you want it to really be two switches. The "throw" means how many different options there are. DPST is basically an on/off switch, DPDT lets you switch between two different outputs, DPTT is between three things etc. So when you say 2pole 6way, that means you'd have 6 different selections and you'd be controlling two mono switches.
So you could get a dual pole switch with as many throws as you want to switch between, so DPDT if you have two things to select between for example. Another way to do it would be to use relays. If you want just plain jane switching then a dual pole multi throw switch is much easier and simpler to implement, but if you wanted to switch balanced and have indicator lights or possible do other things then you'd need a 5+ pole switch - once you start getting into more specialized things it's hard to find what you're looking for. Relays are helpful with this because you can use a 1pole multi throw switch and run all the relays you want to energize in parallel off the single pole of the switch. They're probably way to complicated for what you want to do, but it's something to keep in mind for future projects.
