Strongest Base --
Be(OH)2 , Mg(OH)2 , Al(OH) 3 , Si (OH) 4
The Mg, Al and Si belong to third period of the group and as we move from Mg to Si, the size decreases as a result the tendency to lose electrons also decreases.
Be and Mg belongs to same group, as we move from Be to Mg the size increases as a result tendency to lose electrons increases.
Thus, these two factors determine that Mg(OH)2 is the strongest base among the given hydroxides.