Phenolphthalein is an indicator, a chemical which changes colour depending on whether it reacts with an acid or a base. In basic solutions, it will appear pink, and clear in acidic solutions. X turns pink on addition of phenolphthalein, therefore, it is basic in nature and Y does not change colour so, it is acidic in nature.
Sodium carbonate is formed by the combination of Sodium hydroxide (strong base) and carbonic acid (weak acid). Hence, it is basic in nature.
Ammonium chloride (NH4‌Cl) is the salt of a strong acid, hydrochloric acid (HCl), and a weak base ammonium hydroxide (NH4‌OH). Hence an aqueous solution of ammonium chloride is acidic in nature.