From the Super Mario Wiki, the Mario encyclopedia
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The player first needs to use a Springboard on the left to reach the Mini-Mario above, and then return back down after activating it. They then need to move right and press the blue Color Switch so the Mini-Mario can land on it after using a Springboard, and then they need to be led back to the start and the player needs to press the red Color Switch to trap the Mini-Mario. After moving right and pressing the yellow Color Switch, the player has to return to the Mini-Mario and lead it over the new platform over the spikes. Progressing right, the player can lead the Mini-Mario into a hole above, allowing it to jump and unite with the player and they can now open the locked door to the left.