Answer:
These are the events in chronological order:
750 B.C. Greek city states flourish with shared Greek identity
27 B.C. Rome becomes an empire and Augustus becomes its first emperor.
395 A.D The Roman Empire is divided into the Eastern and Western empires
476 A.D. Invasions bring about the fall of the Western Roman Empire.
We can spot the pattern here: B.C. means "Before Christ". B.C. refers to the events that ocurred before the birth of Christ, which has been established at the year 0.
A.D. means Anno Domini, and refers to all the years taht ocurred after the birth of Christ.
This is why the Greek city states flourished before the fall of the Western Roman Empire.