The Little Sorcerers

The Little Sorcerers is a quest in Legend of Mana.

Solution
When you leave your house after completing your first Event, you will trigger this Event. After the little conversation, enter Domina.

On the Domina Map head to the point at the far left. This will take you to the Outskirts of Domina. Proceed to the upper left of this area and you will see a cool looking pumpkin patch and two sorcerers.

Battle the two kids and dodge their magical attacks. After the battle tell Bud that you want him to be your apprentice.