Below is a walkthrough for the Upgrade Armor task in Rune Factory 5.
Client: Murakumo
Objective: Upgrade some armor
Reward(s): Silver x1
After accepting the task at the Task Board, Murakumo will task you with upgrading some armor. Head to your Crafting Table and select the upgrade armor. Please note that you cannot upgrade armor that is currently equipped. Select the armor piece you wish to upgrade and the material you wish to use then upgrade the armor. Pretty much anything works, I used Scarp Metal for this one. When you are done, return to the Task Board to complete the task.