The first four ionization energies for an imaginary element, xz, are e1 = 102 kcal, e2 = 186 kcal, e3 = 4021 kcal, and e4 = 4862 kcal. the most probable number of valence electrons as indicated by this ionization data is:

The ionization energy is the minimum energy required to remove an electron. If you look at the first ionization energy and second ionization energy, they are both comparatively smaller than the third and fourth ionization energy. The valence electrons are the outermost electrons which means that they are easier to remove. Since the first and second ionization energies are small, the atom probably has 2 valence electrons.