Step (i): exhaustive nitrile reduction. Excess LiAlH${}_4$ reduces each of the four nitrile groups to a primary amine. The intermediate is the tetraamine $({\text{H}}_2{\text{NCH}}_2{)}_2\text{CH-CH}({\text{CH}}_2{\text{NH}}_2{)}_2$.

Step (ii): condensation with acetophenone. Each primary amine reacts with one molecule of acetophenone (PhCOCH${}_3$) to form an imine (Schiff base) with loss of water: ${\text{R-NH}}_2+{\text{PhCOCH}}_3\to {\text{R-N=C(CH}}_3)\text{Ph}+{\text{H}}_2\text{O}$. Four imines form, one for each amine.

Counting sp${}^2$ carbons in P. Each of the four imine units contributes: (i) one imine carbon $\text{C}=\text{N}$, sp${}^2$, and (ii) one phenyl ring with six sp${}^2$ carbons. The methyl carbon attached to the imine is sp${}^3$ and is not counted. Per unit: $1+6=7$ sp${}^2$ carbons. Total for four units: $4\times 7=28$.

The central two CH carbons and the four CH${}_2$ carbons of the aliphatic backbone are sp${}^3$ and contribute zero.

Answer: 28.