Works much like the Birthday quest. The game does not keep track of where you actually got the item, so if you already have one, you can turn it in for the reward. The NPC named in the posting will always have what the poster wants in their inventory. When you meet with the target NPC you will notice that you can trade with them, similar to how you can trade with adventurers. You can pickpocket or trade with the NPC to get the item. Because what the poster wants is usually very cheap, and because you do not need to leave the city or take any risk (unless you are stealing), this is usually a surprisingly easy quest. You can usually buy one unit of any alcohol or use any junk you have in your inventory to trade for the item.