Make sure you complete the mission Gilbert: Love is Blind before facing this one, or that mission will no longer be available. Go to Geo, at the Fruit Parlor Cafè. You'll see Gilbert talking to Nathinja. She will say that her students are boycotting school and Gilbert volunteers to get them back to class. When she leaves, the mission will start. Talk to Gilbert and agree to help him.
Now you have to talk to all the students scattered around the city and convince them to return to school. Finding them all is easy. You will be able to respond to each student with two options, sometimes even several times. If you give the right answer, the student will agree to return to school, if you get it wrong, just talk to him again and select the other option. Maybe talk to everyone a second time to make sure you've convinced them. You must search the areas of the city to talk to all the students: the Café where you started the mission, Mall Avenue, and the Magic Academy. You can instead ignore the Palace of Arts, there are no students here. However, there is one student who you can only convince after talking to all the others, he is in the Instruments Shop. When you have done so, he will also agree to return to school and you’ll see Gilbert and Nathinja talking outside Geo's main walls. Gilbert will be turned to stone and your mission will end.