The crystal field stabilization energy (CFSE) for $[CoCl_6]^{4-}$ is $18000 \text{ cm}^{-1}$. The CFSE for $[CoCl_4]^{2-}$ will be:

The problem asks for the crystal field splitting energy of a tetrahedral complex ($\Delta_t$) given the splitting energy of the corresponding octahedral complex ($\Delta_o$). According to Crystal Field Theory, for the same metal, the same ligands, and similar metal-ligand distances, the relationship between the tetrahedral splitting energy ($\Delta_t$) and the octahedral splitting energy ($\Delta_o$) is given by the equation:

$\Delta_t = \frac{4}{9} \Delta_o$

Given that $\Delta_o = 18000 \text{ cm}^{-1}$ for $[CoCl_6]^{4-}$, we can calculate $\Delta_t$ for $[CoCl_4]^{2-}$:

$\Delta_t = \frac{4}{9} \times 18000 \text{ cm}^{-1}$ $\Delta_t = 4 \times 2000 \text{ cm}^{-1}$ $\Delta_t = 8000 \text{ cm}^{-1}$

(Note: While the question uses the term 'CFSE', in this context it refers to the magnitude of the crystal field splitting parameter, $\Delta$).