The quest requires me to learn a technique from a disc that he gaves me. BUT. before questing i was wandering and found the shopping plaza and bought the same technique (Resta). So i tought that if u just put the technique on the sub-pallete the quest wou go on. but it seems that it will not, so i'm stuck on this quest.

same also my sub pallets are not changing either when i change weapons

If I recall, you need to set the Tech on a Weapon for it to clear, unless I'm thinking of another one of his COs.

EDIT: I double checked, and it does indeed appear that the Objective specifically is to set a Tech to your Weapon, even though it says "Weapon Palette or Sub-Palette" in the Client Message.