Electronic configuration and magnetic moment:

• In $[\text{Co}(\text{NH}_3)_5\text{Cl}]\text{Cl}_2$, cobalt is in $+3$ oxidation state: $\text{Co}^{3+} = [\text{Ar}]3d^6$.
• Because the coordination sphere contains predominantly strong-field ammine ($\text{NH}_3$) ligands, crystal field splitting energy $\Delta_o \gt P$ (pairing energy).
• All six $3d$ electrons pair up in the lower $t_{2g}$ orbitals: configuration is $t_{2g}^6 e_g^0$.
• Number of unpaired electrons $n = 0$.
• Spin-only magnetic moment $\mu = \sqrt{n(n+2)} = \sqrt{0(2)} = 0.0\text{ BM}$ (diamagnetic).

Determination of hybridization according to VBT:

• $\text{Co}^{3+}$ has ground-state configuration $3d^6 4s^0 4p^0 4d^0$.
• Under the strong ligand field of ammine ligands, the six $3d$ electrons pair up into three $3d$ orbitals ($t_{2g}^6$).
• This leaves two inner $(n-1)d$ orbitals vacant, along with one $4s$ and three $4p$ orbitals.
• These six orbitals undergo $d^2sp^3$ hybridization to accept six lone pairs of electrons from the five $\text{NH}_3$ ligands and one $\text{Cl}^-$ ligand.
• Therefore, the complex is an inner orbital octahedral complex with $d^2sp^3$ hybridization.