Use the arrows above!
Ammonia $NH_3$ is a base. Write the equation of base hydrolysis !
$NH_3$ $+$ $H_2O$ $\rightleftarrows $ $NH_4^+$ $+$ $OH^-$.
The brown precipitate is silver oxide. Equation?
$2Ag^+$ $+$ $2OH^-$ $\rightarrow$ $ Ag_2O$ $+$ $H_2O$.
Redissolution of the silver oxide is due to the formation of diamminesilver(I) complex ion. Equation?
$Ag_2O$ $+$ $4NH_3$ $+$ $H_2O$ $\rightarrow$ $ 2Ag(NH_3)_2^+$ $+ $ $2OH^-$
An aldehyde is converted into carboxylic acid by oxidation. Equation?
$RCHO$ $-$ $2e^-$ $+$ $H_2O$ $\rightarrow$ $ RCOOH$ $ +$ $2H^+$
This reaction proceeds under basic conditions here and in addition the carboxylic acid is converted to carboxylate ion . Oxidation equation?
$CHO$ $-$ $2e^-$ $+$ $ 3OH^-$ $\rightarrow $ $RCOO^-$ $ +$ $2H_2O$
The diamminesilver cation is reduced to silver (mirror) by releasing the complexant. Reduction equation?
$Ag(NH_3)_2^+$ $+$ $2e^-$ $\rightarrow$ $ Ag$ $ +$ $2NH_3$
Establish the complete redox system !
$RCHO$ $-$ $2e^-$ $+$ $ 3OH^-$ $\rightarrow$ $ RCOO^-$ $ +$ $2H_2O$
$Ag(NH_3)_2^+$ $+$ $2e^-$ $\rightarrow$ $ Ag$ $ +$ $2NH_3$ | $\cdot 2$
$2Ag(NH_3)_2^+$ $+$ $RCHO$ $+$ $ 3OH^-$ $\rightarrow$ $ Ag$ $ +$ $2NH_3$ $+$ $RCOO^-$ $ +$ $2H_2O$