Source: Cotton & Wilkinson, Advanced Inorganic Chemistry, III edition 1972.
#Mo# neutral atoms have configuration #[Kr]4d^5s^1#. By giving away three electrons we could expect both #d^2# and #d^3# configurations, #[Kr]4d^2s^1# and #[Kr]4d^3s^0#, for the Mo(III) species. We cannot say which one is energetically stabler without considering the ligands and their geometry around the #Mo# atom. The 3+ oxidation state is not one of the most stable states of Mo, and the few reported complexes are octahedral. Thus the #d^3# configuration minimizes the repulsion of #4d# orbitals' lobes with the ligands better than the #d^2s^1# does, as specified below.
Scientific knowledge of chemistry is based on measured properties of known and real substances, not on school talk&chalk teacher's omniscient speculation, or #Mo^"3+"# "naked" and useless ions, isolated in the empty space.
So let's welcome relevant information of really existing chemicals: a yellow ion #Mo(H_2O)_6^"3+"# ion can be obtained, but it is unstable because sensible to oxidation, whereas chlorocomplexes of Mo(III), as #MoCl^"3-"#, form red precipitates with the biggest alkali metal ions, as in #K_3MoCl_6# which are stable red crystals in absence of humidity.
The magnetic behavior of #MoCl_6^"3-"# corresponds to an electronic configuration #t_"2g"^3#. The magnetic momentum is 3.8 BM (Bohr magnetons) meaning there are three (d) unpaired electrons.
The #2g# subscript in #t_"2g"^3# means that the three unpaired d electrons occupy the three 4d obitals which haven't lobes directed in the x, y, z directions. This in turn confirms that the six halogen atoms are octahedrically coordinated around the central metal atom.
If you want to learn more about the split of the five d orbitals under the octahedral coordination, search the Crystal Field Theory .
Cotton & Wilkinson report also the species #[Mo(NCS)_6]^"3-"# as being octahedral and #d^3#.
Chemistry having to do with real, coloured substances, is quite more interesting. On the other side a kind of "school chemistry" dealing with only theoretical issues does not exist at all out of school.
