The entire reign of Darius III is centred on the battle with the Greek king, Alexander the Great. Darius III ruled the Persian Empire from 336–330 BC. He has to acknowledge Alexander the Great as his superior. The Persian Empire disappears and the Greek Empire takes its place as Alexander the Great overwhelms the Persian Empire with his army.
This verse tells us what we have seen before in the prophecies of Daniel, namely that Alexander arises swiftly but also dies suddenly. Then his kingdom will be divided into four parts. It will not be divided among his posterity. His children (one legitimate and one illegitimate) will be killed. His great empire will be divided among four generals and thus will not belong to any of his children. None of those four kingdoms becomes as powerful as Alexander’s empire once was. Alexander the Great died in 323 BC at the age of 32.
4 And as soon as he has arisen, his kingdom shall be broken and divided toward the four winds of heaven, but not to his posterity, nor according to the authority with which he ruled, for his kingdom shall be plucked up and go to others besides these.