After reaching level 50 of level E mineral gathering, Colek will offer this quest.
The goal of this quest is to gather 20 of each type of grade E mineral (except Astantine, which is only dropped as a random event from other minerals).
It also helps to know that only certain minerals can be collected in an area. For example, Hermit's Hideout on East Bahran Island has Panadium and Artrium. More Artrium can be found near Akhma Cave in the same area.
After completing the quest, you will be able to gather grade D minerals.