The reaction you provided is:
\[ \text{Mg(OH)}_2 + 2\text{HNO}_3 \rightarrow \]
This is an example of a double displacement reaction (also known as a double replacement reaction). In this reaction, the hydroxide ions (OH⁻) from magnesium hydroxide react with the hydrogen ions (H⁺) from nitric acid, leading to the formation of water and magnesium nitrate.
So, the correct answer is:
double displacement