Balance the reaction.
${\text{N}}{{\text{H}}_4}{\text{Cl}} + {\text{Ca}}{\left( {{\text{OH}}} \right)_2} \to {\text{CaC}}{{\text{l}}_2} + {\text{N}}{{\text{H}}_3} + {{\text{H}}_2}{\text{O}}$

Hint- Here, we will proceed by checking whether the given chemical reaction is balanced or not. Then, we will find out the atoms which are not balanced and will balance them one by one till all of the unbalanced atoms are made balanced.

Complete step-by-step answer:
In the given chemical reaction, ammonium chloride (${\text{N}}{{\text{H}}_4}{\text{Cl}}$) is mixed with calcium hydroxide (${\text{Ca}}{\left( {{\text{OH}}} \right)_2}$) to produce calcium chloride (${\text{CaC}}{{\text{l}}_2}$) along with ammonia (${\text{N}}{{\text{H}}_3}$) and water (${{\text{H}}_2}{\text{O}}$). The chemical reaction is shown below .
${\text{N}}{{\text{H}}_4}{\text{Cl}} + {\text{Ca}}{\left( {{\text{OH}}} \right)_2} \to {\text{CaC}}{{\text{l}}_2} + {\text{N}}{{\text{H}}_3} + {{\text{H}}_2}{\text{O}}$
Clearly, in the above chemical reaction, in the LHS of the reaction, there are 1 Nitrogen atom (N), 6 Hydrogen atoms (H), 1 Chlorine atom (Cl), 1 Calcium atom (Ca) and 2 Oxygen atoms (O) whereas in the RHS of the reaction, there are 1 Nitrogen atom (N), 5 Hydrogen atoms (H), 2 Chlorine atom (Cl), 1 Calcium atom (Ca) and 1 Oxygen atoms (O). So, the number of atoms of hydrogen, chlorine and oxygen are not the same on both sides of the given chemical reaction. That’s why the given chemical reaction is not a balanced chemical reaction.
By replacing ${\text{N}}{{\text{H}}_4}{\text{Cl}}$ by ${\text{2N}}{{\text{H}}_4}{\text{Cl}}$ in the given chemical reaction, we get
${\text{2N}}{{\text{H}}_4}{\text{Cl}} + {\text{Ca}}{\left( {{\text{OH}}} \right)_2} \to {\text{CaC}}{{\text{l}}_2} + {\text{N}}{{\text{H}}_3} + {{\text{H}}_2}{\text{O}}$
Clearly, in the LHS of the above chemical reaction, there are 2 Nitrogen atoms (N) whereas in the RHS of the above chemical reaction, there is only 1 Nitrogen atom so in order to balance the nitrogen atoms we will replace ${\text{N}}{{\text{H}}_3}$ by ${\text{2N}}{{\text{H}}_3}$ in the LHS of the last chemical reaction obtained.
${\text{2N}}{{\text{H}}_4}{\text{Cl}} + {\text{Ca}}{\left( {{\text{OH}}} \right)_2} \to {\text{CaC}}{{\text{l}}_2} + 2{\text{N}}{{\text{H}}_3} + {{\text{H}}_2}{\text{O}}$
Clearly, in the LHS of the above chemical reaction, there are 2 oxygen atoms (O) whereas in the RHS of the above chemical reaction, there is only 1 oxygen atom (O) so in order to balance the oxygen atoms we will replace ${{\text{H}}_2}{\text{O}}$ by ${\text{2}}{{\text{H}}_2}{\text{O}}$ in the LHS of the last chemical reaction obtained.
${\text{2N}}{{\text{H}}_4}{\text{Cl}} + {\text{Ca}}{\left( {{\text{OH}}} \right)_2} \to {\text{CaC}}{{\text{l}}_2} + 2{\text{N}}{{\text{H}}_3} + 2{{\text{H}}_2}{\text{O}}$
Clearly, in the LHS of the above chemical reaction, there are 10 hydrogen atoms (H) which is the same as the number of hydrogen atoms in the RHS of the above chemical reaction.
Therefore, the balanced chemical reaction corresponding to the given chemical reaction is
${\text{2N}}{{\text{H}}_4}{\text{Cl}} + {\text{Ca}}{\left( {{\text{OH}}} \right)_2} \to {\text{CaC}}{{\text{l}}_2} + 2{\text{N}}{{\text{H}}_3} + 2{{\text{H}}_2}{\text{O}}$

Note- In this particular problem, in the first step of balancing the given chemical reaction we have replaced ${\text{N}}{{\text{H}}_4}{\text{Cl}}$ by ${\text{2N}}{{\text{H}}_4}{\text{Cl}}$ because in the RHS of the given chemical reaction, there are 2 chlorine atoms where in the LHS there was only 1 chlorine atom. That’s why in order to balance the chlorine atoms this replacement was done.