Final answer:
The Romans were known for exporting various goods, but the highly valued item mostly exported by the Romans to far-reaching places like China is 'glass bottles'. This shows the significance and wide-reaching influence of Roman glass production.
Step-by-step explanation:
Considering the contextual information provided and historical records, the Romans were famous for several exports, but regarding the item sought in this multiple-choice question, and looking at the vast extent of trade during that era, it's clear that Roman glassware ended up as far as China. The Romans did export various goods including textiles and pottery, but when focusing on the item that was mostly exported by the Romans and highly valued around the world, including in China, the correct answer is glass bottles (option a).
Roman glass production was a significant industry, and glass items were prized commodities that were traded far and wide. For a time, central Italy was the hub of glass manufacturing before it shifted northward to Gaul and Germany in the second century CE. Even after a decline in local production, Roman-designed glass continued to influence styles, such as those from Islamic luxury glass which were exported both to Europe and China after the fall of the Roman territories.
The Romans did not export Buddhism; it was a religion that spread from India to other parts of Asia, including China. Rugs were not specifically mentioned as a Roman export in the provided materials. And while porcelain was a highly prized export, it was famously produced and exported by the Chinese, not the Romans.