Phthalimide undergoes the following transformations:
In the presence of KOH, the acidic hydrogen of phthalimide is removed, forming the phthalimide anion.
The phthalimide anion then reacts with benzyl chloride via an S\(_N2\) reaction, leading to the formation of product 'P'.
In product 'P':
The benzene ring contributes \(3 \, \pi\)-bonds.
Each carbonyl group (C=O) provides \(2 \, \pi\)-bonds, giving a total of \(4 \, \pi\)-bonds for both groups.
The benzyl group attached to nitrogen contributes \(1\) additional \(\pi\)-bond.
Thus, the total number of \(\pi\)-bonds in product 'P' is:
\[3 + 2 + 2 + 1 = 8\]