First you write the “molecular” equation, then the ionic equation, and finally the net ionic equation.
You can read about these equations at
http://socratic.org/questions/what-is-the-net-ionic-equation-of-the-reaction-of-fecl2-with-naoh
Here are the steps for your reaction.
1. Write the molecular equation
We write the equation as if all the reactants were molecules.
2HNO₃(aq) + Mg(OH)₂(s) → 2H₂O(l) + Mg(NO₃)₂(aq
2. Write the ionic equation
We write all the soluble strong electrolytes as ions. H₂O is a weak electrolyte, so we write it as a molecule. Mg(OH)₂ is insoluble, so we write it as a molecule as well.
2H⁺(aq) + 2NO₃⁻(aq) + Mg(OH)₂(s) → 2H₂O(l) + Mg²⁺(aq) + 2NO₃⁻(aq)
3. Write the net ionic equation
Here, we cancel all species that appear on both sides of the equation. We cancel the NO₃⁻ ions.
The net ionic equation is
2H⁺(aq) + Mg(OH)₂(s) → 2H₂O(l) + Mg²⁺(aq)
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