Step 1: First reaction with aqueous KOH.
2,2-Dichloropropane undergoes hydrolysis with aqueous KOH to form acetone (propanone).
Step 2: Reaction with magnesium in benzene.
Acetone reacts with magnesium to form a Grignard-type intermediate which couples to form a diol.
Step 3: Acidic hydrolysis.
On acidic work-up, the coupled product forms pinacol.
Step 4: Conclusion.
Therefore, the final product B is pinacol.