There is no quest or anything needed to be able to (permanently) add charms to equipment. I have the Xbox version and never used charms, but IIRC selecting equipment and hitting the A button would give the equip/unequip option, as well as charm (if there were charms and empty charm slots available), 'sent to battle tower' (when obtained) and destroy (unless it was a quest item).
Do you have a piece of equipment with one or more empty charm slots? Try one your character is wearing, if you were trying it in the inventory, or vise versa. By level 21 you should be getting charm and enchantment slots on most equipment.
Do you have charms in your inventory? If you have the battle tower, you can not add charms that are in the chest there, just from your character's inventory. Alchemy and enchantment ingredients can be used from the battle tower chest.
Did you check the manual? Other than a paper manual with the retail release, there should also be a pdf (manual_en.pdf) on the DVD, or with the Steam version in the folder below (I assume something similar for other digital distributions).
..\Program Files\Steam\steamapps\common\divinity ii - dragon knight saga
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