Let's match the polymers with their respective polymerization methods:
- P. Linear low density polyethylene is synthesized through the Ziegler-Natta method, hence \( P-2 \).
- Q. Nylon 6 is synthesized through Ring opening polymerization, so \( Q-1 \).
- R. Styrene-butadiene rubber is made using Emulsion polymerization, therefore \( R-4 \).
- S. Aromatic polyamide is synthesized by Condensation polymerization, hence \( S-3 \).
Thus, the correct answer is option (A).