In $[CoF_6]^{3-}$, the central metal ion Co is in the +3 oxidation state, which has a $3d^6$ electronic configuration. Since $F^-$ is a weak field ligand, the crystal field splitting energy is less than the pairing energy ($\Delta_o < P$). Thus, it forms a high-spin complex with the configuration $t_{2g}^4 e_g^2$. It has 4 unpaired electrons ($n=4$). The spin-only magnetic moment is $\mu = \sqrt{4(4+2)} = \sqrt{24} \approx 4.9$ BM.

In $[Co(C_2O_4)_3]^{3-}$, Co is also in the +3 oxidation state ($3d^6$). However, the oxalate ligand ($C_2O_4^{2-}$), being a chelating ligand, acts as a strong field ligand when complexed with $Co^{3+}$. This causes the electrons to pair up ($\Delta_o > P$), resulting in a low-spin complex with the configuration $t_{2g}^6 e_g^0$. It has 0 unpaired electrons ($n=0$), meaning it is diamagnetic with a magnetic moment of 0 BM.