If an acid is added to an equilibrium mixture containing Mg(OH)2 in water, the acid will react with the basic Mg(OH)2 to form water and a salt, shifting the equilibrium towards the left, according to the following reaction:
Mg(OH)2 (s) + 2H+ (aq) ↔ Mg2+ (aq) + 2H2O (l)
As a result, the concentration of Mg2+ ions in the solution will decrease, and the concentration of hydroxide ions (OH-) will increase. This will lead to an increase in the pH of the solution, making it more basic.
If the acid is strong and added in sufficient amounts, it can completely neutralize all the Mg(OH)2 in the solution, resulting in a solution containing only the salt of the acid and Mg2+ ions. The pH of the solution will then depend on the acidity/basicity of the salt formed.
Overall, the addition of an acid to an equilibrium mixture containing Mg(OH)2 in water will disrupt the equilibrium and cause a shift towards the left, resulting in a decrease in the concentration of Mg2+ ions and an increase in the concentration of OH- ions, which will make the solution more basic.