Final answer:
The common method for becoming emperor in ancient Rome that contributed to its decline was military conquest. This method led to political instability and was one of the factors of the Empire's downfall.
Step-by-step explanation:
A common way for people to become emperor in ancient Rome, which contributed to its decline, was b) Military conquest. Over time, Roman political culture evolved from a monarchy to a republic and finally to an empire, with each stage having different methods of selecting leaders. In the latter years of the Empire, a combination of military power, political intrigue, and the assassination of rivals often determined succession rather than hereditary means or democratic processes. This reliance on military force led to periods of political instability, which, alongside other factors like economic troubles and external pressures, contributed to the decline of the Roman Empire.