Step 1: Concept
Buna-S is a synthetic copolymer also known as SBR (Styrene-Butadiene Rubber).
Step 2: Meaning
The name "Buna-S" comes from Butadiene (Bu), Sodium (Na) as the catalyst, and Styrene (S).
Step 3: Analysis
Monomer X is 1,3-Butadiene. Monomer Y must be Styrene, which has the chemical formula $C_{6}H_{5}CH=CH_{2}$.
Step 4: Conclusion
Therefore, Y is Styrene, represented by option B.
Final Answer: (B)