The chemical which is least soluble among the above four is 

Let me give you the solubility of all the chemical mentioned... 

->BeF2 : is soluble in water due to evolution of large hydration energy, when it is dissolved in water, which is sufficient enough to overcome the lattice energy of the Berylium Flouride, as for a compound to be soluble in water, the lattice energy of the compound must be less than the hydration energy evolved upon dissolution in water.

-> mgcl2: Magnesium chloride is the chemical compound with the formula MgCl2. It is an inorganic salt, which is highly soluble in water.

->CaF2: is not soluble in water due to extremely high lattice energy.CaCl2 is fairly soluble in water as it's lattice energy is lower compared to CaF2.

-> mgf2: Magnesium fluoride is an inorganic compound with the formula MgF2.insoluble in water and alcohol, soluble in nitric acid

As we can see the solubility nature of chemicals we can say that bef2 and mgcl2 are is least soluble than As the other two i.e, CaF2, Mgf2 are insoluble in water