Persona 3 FES Request 58
For this Request you will need to take Elizabeth on a date to the Naganaki Shrine after school. To start this request you will need to enter The Velvet Room in the Paulownia Mall after school and speak with Elizabeth. After that the whole request is pretty much just a cutscene for you to enjoy.
This is the third quest in a chain that involves taking Elizabeth out to different places on dates. You must complete this task to unlock the later ones in the chain. Each will become available at different times throughout the year if you've completed the previous request required.