After completing (or failing) the quest Agent of Chaos, the player will receive a miscellaneous objective to check in with Valerine.
When they ask her about more Emissary work, she will start this quest.
Valerine will tell the player of a visiting Emissary that is searching for a gift for his wife. She needs the player to convince him to commission the Bards College to write a sonnet as that gift.
The player will then be given the objective to meet Valerine in the market area of Solitude.
When the player reaches Valerine's meeting point, she will introduce the player to Vinnus.
Being that Vinnus is a skilled Emissary himself, simply using the same tone each time will not be successful. In addition, the goal isn't for the player to make him like them, but to steer him away from other gifts and towards the commission.
The optimal solution is to choose the option that disdains each gift idea until reaching the final choice where the player's best option is to tell Vinnus he knows his wife best, though at this point if the player dissuaded all other options, any choice would be successful.
The series of choices for the best result is: Whimsical, Dramatic, Heartening, Heartening.
Upon reporting back to Valerine, the player will receive 1000 gold for the best result, 500 gold for the neutral result, and nothing for failure.
The next mission will become available a short while after this is finished. The player will be prompted with a miscellaneous objective to remind them to speak to Valerine again.