The reaction in ${\text{NH}}_{\text{4}}{\text{OH\hspace{0.17em}and\hspace{0.17em}NH}}_4\text{C}l$ buffer is ${\text{NH}}_{\text{4}}\text{OH}+{\text{H}}^{+}\to {\text{NH}}_4^{+}+{\text{H}}_{\text{2}}\text{O}$, this is due to the addition of

${\text{NH}}_{\text{4}}\text{OH}+{\text{H}}^{+}\to {\text{NH}}_4^{+}+{\text{H}}_{\text{2}}\text{O}$

The ${\text{H}}^{+}$ion added to the buffer are thus removed as ${\text{H}}_2\text{O}$. Hence the pH of the solution does not change.