Below is a walkthrough for the Build a Monster Barn task in Rune Factory 5. Please note that this task showed up for us on the Task Board after we completed the Find My Mommy main task.
Client: Ryker
Objective: Build a Monster Barn
Reward(s): New Shop Inventory (Fodder Seeds), Brush
After accepting the task, Ryker will show up to give you the details on the Monster Barn. He will also give you enough materials to have one built at Studio Palmo. Make your way there and choose the renovate option. You can then choose to have Monster Barn A built on the Farm Dragon. Return to the Task Board to complete the task.