A $Z^{2+}$ ion has a $2+$ charge, meaning it has lost 2 electrons compared with the neutral atom.

We are told the ion contains 18 electrons.

For the neutral atom $Z$:

$$\text{number of electrons in neutral } Z = 18 + 2 = 20$$

In a neutral atom, the number of protons equals the number of electrons. Therefore, the neutral atom $Z$ has:

$$20 \text{ protons}$$

When an atom forms an ion, the number of protons does not change; only the number of electrons changes. So the ion $Z^{2+}$ also contains:

$$20 \text{ protons}$$

Therefore, the correct answer is:

$$\boxed{20}$$

Answer: A) 20