From the Super Mario Wiki
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The player first has to move past a Thwomp and press the yellow Color Switch, and then avoid a Thwimp and a second Thwomp. At the floating stair platform, the player has to do a Handstand Double Jump to get onto it, and then use the ropes above or another Handstand Jump to jump to the platform with the Mini-Mario. The player then needs to head back toward the start, avoiding the Thwomps and Thwimp once more, this time with the Mini-Mario behind them. Once the player and Mini-Mario are up the yellow stairs, they need to press the red Color Switch. Using them to reach a pair of ropes, the player has to climb over a platform, triggering the Thwomp to fall, and quickly fall onto the platform with the locked door so the Mini-Mario will jump across and unlock it.