From the Super Mario Wiki
Badminton (Doubles) is a Court & Field Sports Event that appears in the Nintendo 3DS version of Mario & Sonic at the London 2012 Olympic Games. The objective of the event is to score three points against the opponent first.
In the game's story mode, Badminton (Doubles) appears as the challenge of Sonic Episode 2, The Ghostly Tower, in which Sonic and Tails must beat King Boo and a Boo. It also appears as part of the fifth challenge of Heroes Episode 5, The Promise to Toad, in which Mario and Sonic must beat Fog Imposters of Luigi and Tails in it, as well as in Table Tennis (Doubles) and Sailing - 470 (Pair).
In this event, the player must pick two characters from the Heroes category, and competes against a pairing of the other two in the final, with a pair of Koopa Troopas and a pair of Chao taking the bottom two spots, meaning that it is impossible for the player to get any position lower than second in this event. In this event, the player serves and returns the shuttlecock by sliding down on the touch screen. The player is the first to serve in the event, with the server being on the side that lost the last point from then on. The player may serve the shuttlecock at any time. When the shuttlecock is returned to the player, they must slide down on the touch screen when it flashes red to return it to the other side. If the player either fails to slide down or does so too late or too early, they will miss the shuttlecock and the point will be awarded to the other team. If the shuttlecock is returned with bad timing, the other side will have the opportunity to perform a powerful shot that it much harder to return by successfully returning the shuttlecock, which will then be surrounded by a flame effect. A rally count is kept throughout the event, and the first team to score three points against the other wins. Toad acts as a referee in this event.
1) Hit: Slide ↓ on the touch screen.