Are any of those 12 teams playing against each other? In other words, are you looking at 6 games involving 12 teams with sides and totals?
If this is the case, then you can form 59,136 parlay combinations.
Take 24x22x20x18x16x14 and divide it by 6x5x4x3x2x1.
Your first team can be any of the 12 sides or 12 totals, giving you 24 possibilities. But once you choose that first side (or total) you must eliminate the other side or total from future choices since you cant parlay both an over and under in the same game for example. Your second choice in the parlay comes from the remaining 22 possibilities, etc....
But, if you have 12 teams, where all 12 teams are playing other teams not amongst those 12, then you have 1,423,796 possible 6-team parlays.
The calculation here is much more involved since you have to break it down into categories by how many sides and how many totals.
If you meant something other than the 2 scenarios I gave, let me know. I can rework the numbers from there.
p.s. Glad to be a member of the forum.