This quest is available starting Chapter 30.
Go to the Gurak Castle. Talk to man guarding the gate. Listen to the knight mutter to himself about wanting to read something. Return to Lazulis Island. A girl in blue is standing near the East Gate. Talk to her to receive the fashion magazine. Go to Gurak Castle. When you leave Gurak Castle, you have to go back to the knight. Talk to him and give him the magazine. In return, he asks you to deliver a letter to his girlfriend. Give the letter to the girl for your reward.
Reward: Dragon Fang