Equipment Refine is a quest unlocked as soon as the player has completed Recycle Equipment.
The objective is to get used to the mechanics of item refinement. It is completed as soon as the player opens the Blacksmith window and refines any item. It is not neccessary to actually swap the stats for the refined ones.
Click on the [Blacksmith] -> Select [Refine] -> Refine any equipment once. Equipment attributes will be reset after refinement.
The player is rewarded 10500 Gold.