Step 1: Understanding the reaction for 'x'.
The product 'x' is obtained from benzene by reacting it with carbon monoxide and hydrogen chloride in the presence of cuprous chloride, which is the reaction in the Friedel-Crafts acylation. The product is benzaldehyde (C$_6$H$_5$CHO).
Step 2: Understanding the reaction for 'y'.
The product 'y' is the major product obtained by reacting benzene with ethanoyl chloride in the presence of anhydrous AlCl$_3$, which is the Friedel-Crafts acylation reaction. The product formed is acetophenone (C$_6$H$_5$COCH$_3$).
Step 3: Reaction between x and y.
When benzaldehyde (x) and acetophenone (y) are heated in the presence of an alkali, they undergo the benzoin condensation reaction, resulting in benzoin (C$_6$H$_5$CHOHCOC$_6$H$_5$).
Step 4: Counting the $\pi$ electrons in z.
Benzoin (z) contains two benzene rings, and each benzene ring contributes 6 $\pi$ electrons. Thus, the total number of $\pi$ electrons in benzoin is 12.