HBr (aq) + Mg(OH)2 (s) ->

The reaction between hydrogen bromide and magnesium hydroxide will result in the formation of magnesium bromide and water. The reaction can be written as:

`HBr (aq) + Mg(OH)_2 (s) -> MgBr_2 (aq) + H_2O (l)`

However this equation is not balanced as the number of hydrogen atoms on reactant side is 3 (= 2 + 1) and that on the product side is 2. Similarly, there are two atoms of oxygen on the reactant side, while the product side has only 1. Bromine is also unbalanced. To balance all these atoms, on both the sides of the reaction, we can use coefficients. The balanced chemical reaction is given as:

`2HBr (aq) + Mg(OH)_2 (s) -> MgBr_2 (aq) + 2H_2O(l)`

Here, we can see that magnesium replaces the hydrogen atom and bonds with bromine, while the hydrogen ion reacts with hydroxide ion to form water. This is, thus, a double replacement reaction.

Hope this helps.