This page in our guide to GreedFall contains a walkthrough for The Man With the Silver Coin side mission.
Where to start the quest?: The task will automatically start after you complete Coin Guard Merchandise side mission.
Go to the market and talk to each of the merchants. After all, you'll have to convince one of them to help you. You can try to use charisma, or spend 100 pieces of gold. If the trader agrees, you will have to wait 2 days in the game for the situation to develop (1 minute in the game is around 1 second in real time). If you want, you can go back to your home and get some sleep to speed up the time (the campfire icon on the map).
After two days, talk to the merchant. Then hide in the alley behind his stall. Blackmailers will appear - defeat them and loot their bodies. You'll find out about the position of the man with the silver coin. Go to the indicated place and after the cutscene start following the man. Be careful not to get spotted - go far enough behind the man and crouch down to sneak.
After a while, you'll have to fight with the character you're following. You must defeat your opponent and then search his body for clues.
Go to Manfred's and let him know about the results of your quest. For completing the quest you will earn +3 reputation points with the Coin Guard faction, 50 gold pieces, and 1300 XP.