To serve a drink to someone, I think the other Sim has to be in the same room or at least the building. I've done this quest and can't remember if it's the one where the other sim is in the forest with a keg nearby. If it is, you can brew in that keg and serve to them. Another way I often do it is to get the other sim to come to me - when your sim is sitting and eating or drinking, if you click on the sim you want and "Call Over", they'll come to you. Then you can serve a drink from the keg where you are. I find the tavern a good central place for meeting people, but you could also do it from home.