Right answer. Wrong reason. Entropy doesn't enter into it.
To do a VERY detailed answer:
HCl(aq) ==> H^+ + Cl^-
The excess H^+ from the HCl reacts with the OH^- from the ionization of Mg(OH)2 to form H2O. This reduces the concn of OH^- on the right and, by Le Chatelier's Principle, the Mg(OH)2 reaction shifts to the right to replace the OH^- lost by the reaction with HCl. So more of the solid (on the left side of the equation) dissolves to try to restore the OH^- that it had before the HCl messed things up. Remember the Ksp = (Mg^+2)(OH^-)^2 = constant.