HELP! Have a tough math problem

Aug 2015
So, my buddy and I are throwing a lawn olympics party this weekend, and we were trying to put together some brackets, but we ran into a few issues and we need some help.

Here's the deal:

- 12 teams
- 6 different games

*Each team needs to play each game twice.
*We want to have the least amount of repetition playing other teams. We'd want to have each team play each other team once, knowing that there would be one team that you'd have to play twice - preferably not on the same game they played earlier.

How the hell do you construct this? Any help you can lend would be awesome, and I'll send pictures of the girls at the party this weekend.