On this page of the Disco Elysium game guide, you will find a detailed walkthrough of the Find your other shoe side task.
In Disco Elysium, the task Find your other shoe requires you to find your missing green snakeskin shoe. Harry must have lost it during a nighttime escapade.
You will receive the task once you find the first shoe in the hotel room (it's on a hanger). Leave the room and head to the balcony - the lost shoe can be found in the spot marked in the above image.