Which is more basic ${\text{Mg}}{\left( {{\text{OH}}} \right)_{\text{2}}}$ or ${\text{Al}}{\left( {{\text{OH}}} \right)_{\text{3}}}$ ?

Hint: (1) Bases are those substances which can liberate hydroxide ions $\left( {{\text{O}}{{\text{H}}^{\text{ - }}}} \right)$ in aqueous solutions and the term basicity refers to the condition of being a base or as the difficulty of an acid to react with a base.
(2) Generally, on going from left to right across a period on the periodic table, the basic character of the hydroxides tends to decrease and on moving down a group from top to bottom on the periodic table, the basic character of the hydroxides tends to increase.

Complete step by step answer: The given hydroxides are magnesium hydroxide ${\text{Mg}}{\left( {{\text{OH}}} \right)_{\text{2}}}$and aluminium hydroxide ${\text{Al}}{\left( {{\text{OH}}} \right)_{\text{3}}}$. Both magnesium hydroxide ${\text{Mg}}{\left( {{\text{OH}}} \right)_{\text{2}}}$and aluminium hydroxide ${\text{Al}}{\left( {{\text{OH}}} \right)_{\text{3}}}$are the hydroxides of elements of the third period, of magnesium and aluminium respectively. As basicity decreases from left to right across a period, therefore, the basicity of the hydroxides of third period elements will also decrease from left to right.
The third period consists of sodium, magnesium, aluminium, silicon, phosphorus, sulphur, chlorine and argon. Since aluminium comes after magnesium across the third period, therefore, the basicity of the hydroxide of aluminium will be less than the basicity of the hydroxide of magnesium. In fact, aluminium hydroxide is amphoteric in nature. Therefore, magnesium hydroxide is more basic than aluminium hydroxide.

Note: The basic character of oxides also decreases across a period and increases down a group. Across a period, the tendency to lose electrons decreases and so the metallic character also decreases. Since metals from basic oxides and non-metals form acidic oxides, therefore, the basic character of oxides decreases across a period.