$\mathrm{Na}+{\mathrm{Al}}_2{\mathrm{O}}_3\stackrel{\text{ High temperature }}{⟶}\mathrm{X}\underset{\text{ water }}{\stackrel{{\mathrm{CO}}_2\text{ in }}{⟶}}\mathrm{Y}$ compound Y is :

$\mathrm{Na}+{\mathrm{Al}}_2{\mathrm{O}}_3\text{ high temperature }{\mathrm{Na}}_2\mathrm{O}+\mathrm{Al}\frac{{\mathrm{CO}}_2\text{ in }}{\text{ water }}⟶{\mathrm{Na}}_2{\mathrm{CO}}_3$

Therefore, X is Na₂O and Y is ${\mathrm{Na}}_2{\mathrm{CO}}_3$.
As a result, choice C is accurate.