We are given that the metal Y is reddish brown in colour. This metal is copper. The blue solution is Copper Sulphate solution.
Also, zinc is used in protecting iron articles (process called galvanisation). Zinc is more reactive than copper and hence can displace copper from its salt solution. So when substance X is added, Zinc displaces copper to form Zinc Sulphate solution which is colourless. Hence the colour of the solution gets discharged.
X + Blue solution ---> Y + Colourless solution
ie,
Zn(s) + CuSO4(aq) ---> Cu(s)+ ZnSO4(aq)
So, X is Zinc, while Y is Copper. The reaction is a Displacement reaction.