Interesting.
I think that football would be the only sport possible of the 3 named, especially if we were talking about outdoors.
Basketball would be impossible. Six inches of moon dust would reduce the coefficient of restitution (bounce) of a basketball to something approaching zero, thus making dribbling impossible.
The actual size of a cricket arena would have to be enormous. If the average distance from the wicket to the boundary on Earth is (say) 80 metres and the Moon's gravity is approximately 1/6 of that which exists here, then the diameter of the cricket ground would have to be about a kilometre, just to give the batsmen a challenge.
Any smaller and you would just run out of balls. Even at this size, you would be far better lofting the ball into the outfield and having it not quite reach the boundary. Assuming that the average speed of a batsman is around 5 metres per second (and a fielder 7 metres a second), a ball struck to just inside the boundary would reach it in 16 seconds. The batsmen would be able to run 3 whilst the ball was in the air, sorry, vacuum. The fielder would reach the ball in around a minute (if he could find it in the moon dust). His throw would take around 15 seconds to get back to the keeper. In the meantime, the batsmen would have run about 14. Matches would have to be restricted to 5 overs a side, otherwise the scores would be astronomical.
There must be some reason for asking the question. Have you just bought the rights to build the first sporting venue on La Luna ?