Statement-I: ${\left[{\mathrm{SiCl}}_6\right]}^{2-}$ does not exist.

Statement-2: Interaction between lone pairs of chloride ions and ${\mathrm{Si}}^{4+}$ is not very strong and six large chloride ions cannot be accommodated around ${\mathrm{Si}}^{4+}$ due to limitation of its size.

${\left[{\mathrm{SiCl}}_6\right]}^{2-}$does not exist

Because smaller Si cannot hold six big Cl ions due to steric hindrance ${\left[{\mathrm{SiCl}}_6\right]}^{2-}$ is not possible.Because silicon has abundant d-ordinals, it can increase its coordination number beyond four ${\left[{\mathrm{SiCl}}_6\right]}^{2-}$ therefore exists. Contrarily, since C's valence shell lacks any vacant d-orbitals, it is unable to increase its coordination number past four. 

Hence correct option is A.