Mystery Houses are places where you can earn many Green Stars. In this one, you complete challenges in a short period of time to get a Green Star, then warp to the next challenge. Any Green Star you collect, you can keep, but you must collect one after defeating an enemy in order to move on.
In the first room, you must defeat two Galoombas. In the second, two Koopas, in the third, two Cat Goombas. You'll get a Super Bell from one of the Cat Goombas. The fourth room has four Conkdor. Use the Super Bell to defeat them more easily. The fifth and final room has two Fire Bros. After clearing all five room, the Green Stars will be added to your total.