On this page of the Disco Elysium game guide, you will find a detailed walkthrough of the Open apartment door for Evrart task.
In Disco Elysium, during the task Open apartment door for Evrart, you need to do Evrart a favor and open the door to a certain apartment. In exchange, the Union leader will provide you with intel on the hanged man's case.
Start by talking to the NPC known as Call Me Manana and ask him for the key to the apartment you need to open. You will find him near the protest area, sitting on railing and watching the events unfold.
The apartment's door can be found in the other part of the courtyard, behind the Whirling-In-Rags hotel building. To reach your destination, go around the Doomed Commercial Area and walk into the alleyway on the right. Once there, interact with the door and use the key to unlock it.
After completing the task, return to Evrart and relay the information about the open door. Now you'll have the opportunity to learn more about the murder mystery from the Union leader.