a. `[BeF_(4)]^(2-)` exists, but `[BeF_(6)]^(4-)` does not. This can be explained on the basis of valence electronic configuration:
Due to the absence of low-lying `d`-orbitals in beryllium, it cannot expand its coordination number beyond`4`, hence `[BeF_(4)]^(2-)` exists, but `[BeF_(6)]^(4-)` does not.
b. Hydrated beryllium ion exists as `[Be(H_(2)O)_(4)]^(2+)`.
Due to the presence of only four orbitals of equivalent energy in `Be^(2+)` ion and due to the absence of low-lying `d-`orbitals in `Be^(2+)` ion, it can coordinate with four water molecules only, hence hydrated beryllium ion exists as `[Be(H_(2)O)_(4)]^(2+)`.
Whereas in case of magnesium, due to the availability of low-lying d-orbitals of suitable energy, `Mg` can expand its coordination number to 6
Hence, hydrated magnesium ion exists as `[Mg(H_(2)O_(6))]^(2+)`