How would you identify the missing coefficient in the balanced equation and classify the type of reaction?

In order for the reaction to be balanced, the number of atoms of each element must be equal on both sides of the reaction arrow. On the left side, we have

#"Mg": 1#
#"O": 2 + 4 = 6#
#"H": 2 + 2 = 4#
#"S": 1#

And on the right side,

#"Mg": 1#
#"O": 4 + 1 = 5#
#"H": 2#
#"S": 1#

You'll notice that the products side is short two hydrogens and one oxygen. Coincidentally, #"H"_2"O"# just so happens to have that exact element ratio. We need one more #"H"_2"O"# molecule on the products side to balance this equation, so its coefficient becomes

#1# (understood, not shown) + #color(red)(1) = color(blue)(2)#

The balanced chemical equation is thus

#"Mg(OH)"_2 "(s)"+ "H"_2"SO"_4 "(aq)" -> "MgSO"_4 "(aq)"+ color(blue)(2)"H"_2"O(l)"#

This type of reaction is a special kind of double-replacement reaction (or metathesis reaction) called a neutralization reaction, in which an acid and a base react in aqueous solution to form a salt and (usually liquid) water.

There are two primary classifications of reactions
1. Oxidation-Reduction Reactions
2. Metathesis Reactions

Oxidation-Reduction Reactions are characterized by a change in oxidation states of the elements in the reaction.

Metathesis Reactions are Ion Exchange Reactions of the form
AX + BY => AY + BX where A, B, X & Y are Ions in aqueous solution. For a Metathesis Ion Exchange Reaction to occur, a product is formed that leaves the reaction system as a solid precipitate, soluble weak acid or weak base or a gas decomposition product. The Metathesis Reactions reaction is characterized by NO CHANGE in oxidation states of elements in the reaction process.