Why do d-block elements exhibit variable oxidation states?

Hint: Oxidation state means a number which is assigned to an element to represent the number of electrons lost from that element or the number of electrons consumed by the element. Oxidation state can be both positive or negative. d-block elements show more than one oxidation state.

Complete step by step answer:
In case of d-block elements due to presence of electrons at d orbitals, is closer to the outermost shell of the metal. They show variable oxidation state. With increasing the number of electrons of the d orbitals (up to 5 electrons), the numbers of oxidation state increases.
In case of d electrons due to lower effective nuclear charge of attraction the electrons can be removed to form different oxidation states.
For example, Manganese shows oxidation states like \[{\text{ + 2, + 3, + 4, + 5, + 6, + 7}}\]. In these oxidation states, less common \[{\text{ + 3, + 5, + 6,}}\] are easily prepared.

Note:
Actinides are F-block elements(atomic number 89 to103) with the general electronic configuration of outermost shell is \[\left[ {{\text{Rn}}} \right]{\text{5}}{{\text{f}}^{{\text{1 - 14}}}}{\text{6}}{{\text{d}}^{{\text{0 - 1}}}}{\text{7}}{{\text{s}}^{\text{2}}}\]. Where the last electron enters to the inner 5f-orbital of the actinides. Actinides are also known as rare earth metals. Now according to the Aufbau principle(L+S value) the energy order of the orbitals should be \[5f < 6d < 7s\]. but due to the more diffuse orbitals their energy becomes more or less the same. As a result, electrons can be excited easily . Due to this reason actinides shows greater range of oxidation states. But if we consider lanthanides due to comparatively small size of 4f orbital they have limited number of oxidation states