Homoleptic complexes are those in which the central metal ion is surrounded by only one type of ligand. For this case, the complex is [Co(H2O)6]2+.
Co2+ has the electronic configuration [Ar]3d7. The ligand H2O is a weak field ligand, meaning it does not cause a significant splitting of the d-orbitals.
The t2g and eg orbitals are filled based on Hund’s rule of maximum multiplicity: t2g5 eg2.
This configuration results in one unpaired electron in the t2g orbitals.