If x is the number of electrons and y is the number of nucleons...

The given species is ${}^{32}_{16}\textS^{2-}$.

The atomic number $Z$ of sulfur is $16$, which represents the number of protons.

Since the species has a charge of $-2$, it has gained $2$ electrons. Therefore, the number of electrons $x = 16 + 2 = 18$.

The mass number $A$ is $32$. The number of nucleons is the sum of protons and neutrons, which is equal to the mass number. Therefore, the number of nucleons $y = 32$.

Thus, $x = 18$ and $y = 32$.