Structure-based reasoning: Potassium fixation depends on how tightly a clay mineral's layers can trap K\(^{+}\) ions between them.
Vermiculite has a high layer charge and interlayer spacing just right to wedge K\(^{+}\) ions in place, giving it the strongest fixing power. Illite already contains substantial fixed, non-exchangeable K in its structure, giving it the next-highest fixing capacity. Montmorillonite has expanding 2:1 layers but a lower charge density than vermiculite or illite, so it fixes K only moderately. Kaolinite, being a non-expanding 1:1 mineral with almost no interlayer space, fixes essentially no K.
Ranking by this structural logic reproduces the order Vermiculite \(>\) Illite \(>\) Montmorillonite \(>\) Kaolinite, i.e., (D), (A), (B), (C).