Answer
$Zn(OH)_2(s)+2HNO_3(aq)\rightarrow Zn(NO_3)_2(aq)+2H_2O(l)$
Work Step by Step
$Zn(OH)_2(s)+HNO_3(aq)\rightarrow Zn(NO_3)_2(aq)+H_2O(l)$
$Zn$ is in balance. There are 2 $N$ atoms on the right. Add a coefficient of 2 to $HNO_3$ to balance $N$.
$Zn(OH)_2(s)+2HNO_3(aq)\rightarrow Zn(NO_3)_2(aq)+H_2O(l)$
This leaves us with $Zn$ and $N$ balanced, but there are 8 $O$ atoms on the left and 7 on the right. There are 4 $H$ atoms on the left and 2 on the right. Add a coefficient of 2 to $H_2O$ to complete the balancing of the equation.
$Zn(OH)_2(s)+2HNO_3(aq)\rightarrow Zn(NO_3)_2(aq)+2H_2O(l)$
