This page of the Disco Elysium guide contains a detailed walkthrough of the side task: Where is the rest of the armour?
In the Where is the rest of the armour? quest in Disco Elysium, you have to find out what happened to the missing elements of the armor of the murdered man.
In the first place, you should talk to Cuno - a kid who has been throwing rocks at the hanged man from the very start. When you ask where the missing parts of the armour are, the boy will direct you to a man named Manana, who said he was interested in the whole set of ceramic armour.
The conversation will reveal that the armor includes four elements: helmet, boots, gloves and cuirass. It seems that the pants you could buy from Cuno (the Buy FALN Pants task from Cuno) don't fall into this set.
Go back to Cuno and tell him what you learned from Call Me Manana and the quest will be completed.