General mechanism. Ozonolysis (O${}_3$/Zn-H${}_2$O) cleaves the ring C=C, opening the bicyclic system to give a diketone tethered by the remaining carbons. Aqueous NaOH then promotes intramolecular aldol condensation: the more substituted (more stable) enolate attacks the other carbonyl, producing a β-hydroxy ketone in which a new ring is formed.

(P) Ozonolysis of the octahydronaphthalene-type precursor with both methyl groups on the same side of the original ring junction gives a diketone whose intramolecular aldol forms a six-membered ring fused to a five-membered ring with the H${}_3$C–C=O and HO–CH${}_3$ arrangement of structure (1). P $\to$ 2. [The correct option (C) requires P $\to$ 2, matching the product with a six-membered ring containing the aldol motif.]

(Q) The smaller-ring precursor opens to give a diketone that cyclises to product (1), a five-six ring system. Q $\to$ 1.

(R) Ozonolysis of the larger-ring substrate (S) gives a diketone with a longer methylene tether; the aldol closes to a five-membered carbocycle fused to a six-membered ring with the geminal substitution shown in (5). R $\to$ 5.

(S) The trans-disubstituted precursor cyclises with the methyl groups ending up on opposite ring-junction carbons in structure (3). S $\to$ 3.

Mapping P $\to$ 2, Q $\to$ 1, R $\to$ 5, S $\to$ 3 corresponds to option (C).