Answer: A (Al³⁺). A white precipitate with aqueous sodium hydroxide that dissolves in excess narrows the cation down to aluminium (Al³⁺) or zinc (Zn²⁺), because both Al(OH)₃ and Zn(OH)₂ are amphoteric and redissolve in excess NaOH.
The deciding test is aqueous ammonia. Aluminium hydroxide is a white precipitate that is insoluble in excess ammonia, so the precipitate remains. Zinc hydroxide, by contrast, dissolves in excess ammonia to give a colourless solution. Since the precipitate remains in excess ammonia, the cation is aluminium, Al³⁺.
Ca²⁺ gives no precipitate with ammonia (and only a faint white precipitate with NaOH that does not dissolve); NH₄⁺ gives no precipitate with either reagent.
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