Don't forget that to get good neighbors you should make yourself a good and attractive neighbor. If you are looking for something in a neighbor's town that is hard to find, so are other players. I always make sure I always buy the things that I myself have trouble finding and place them in a selected house making it easy for my friends to find. Here the mission to design fashion comes down to finding a neighbor that actually has a fashion studio. The fashion studio can be purchased from the hobby shop south of the park for 2,500 simoleons, don't forget to get your own.
Click on the globe or the party boat to visit your neighbor, select an adult sim for this task.
Click on the house that contains the fashion studio to take your sim to this house. Click on the fashion studio and select option Design fashion.