Step 1: Identify the cumene process.
Cumene reacts with oxygen and then with acidic water. This is the industrial way to make phenol and acetone together.
Step 2: Name A and B.
The products are phenol, which is the acidic one that makes a salt with NaOH, so A is phenol. The other product, B, is acetone.
Step 3: Plan to reduce phenol.
We need to turn phenol into a hydrocarbon, which is benzene. Phenol can be reduced to benzene using zinc dust. So X is Zn.
Step 4: Plan to reduce acetone.
Acetone, a ketone, must be turned into the hydrocarbon propane. The Clemmensen reduction does this using zinc amalgam and HCl. So Y is $Zn(Hg), HCl$.
Step 5: Match the reagents.
So to change A we use $Zn$ and to change B we use $Zn(Hg), HCl$.
Step 6: State the answer.
So X is Zn and Y is $Zn(Hg), HCl$. \[ \boxed{X = Zn,\ Y = Zn(Hg),\,HCl} \]