The reaction pathway you have mentioned involves the conversion of Zinc hydroxide (Zn(OH)2) to Zinc oxide (ZnO), then to Zinc chloride (ZnCl2), then to Zinc metal (Zn), and finally to Silver (Ag).

1. Zn(OH)2 -> ZnO: This is a dehydration reaction where Zinc hydroxide loses water molecules to form Zinc oxide. The balanced equation for this reaction is:
Zn(OH)2 -> ZnO + H2O

2. ZnO -> ZnCl2: This reaction involves the reaction of Zinc oxide with Hydrochloric acid (HCl) to form Zinc chloride. The balanced equation for this reaction is:
ZnO + 2HCl -> ZnCl2 + H2O

3. ZnCl2 -> Zn: This is a reduction reaction where Zinc chloride is heated with Carbon (C) to obtain Zinc metal. The balanced equation for this reaction is:
ZnCl2 + C -> Zn + CO2 + Cl2

4. Zn -> Ag: This reaction involves the displacement of Zinc by Silver in a solution of Silver nitrate (AgNO3). The balanced equation for this reaction is:
Zn + 2AgNO3 -> Zn(NO3)2 + 2Ag

Overall reaction:
Zn(OH)2 -> ZnO -> ZnCl2 -> Zn -> Ag