I was playing today and tried a random feee battle and just saw the 3x3 way.
Can I play 6x6 battles in random free/rating mode?
You can only play 6 v 6 by asking random passersby (or acquaintances or friends) in the PSS for a battle. I don't think there is a way to do a rated battle in 6 v 6. At least in game, you can obviously go on a battle simulator like Pokemon Showdown or something.