NOTE: It's possible but STRONGLY ENCOURAGED NOT to bypass paying the vendors. The means to do so is obviously a leftover developer shortcut, so it may cause future complications. See below for details. You still have to complete the hat guessing game if you pay the vendors.
Travel to each of the vendors listed in the invoice and pay off Tarutaru Sauce's debt by trading the vendors the amount of gil owed.
Peladi Shalmohr is about to burst at the seams from the tab Tarutaru Sauce has run up throughout the city, and has requested that you take care of it. The culprits are hiding somewhere in Western Adoulin...
SPOILER WARNING: Click here for additional details about this story line.