The mysterious potion | Walkthrough HP and the HB Prince Guide

After the cutscene you will be in the library. Head to the painting [1] and use it to get to the Great Staircase. Go to the 7th floor and in one of the corridors you will find a bird cage [2], with an unknown potion recipe inside.

Take it, go back to the Great Staircase and approach the painting [1] leading to the Potions Classroom. Once you're there, approach Hermione [2] and after the cutscene, prepare the potion according to the recipe found.