How did the conquests of Alexander the Great create a new cultural synthesis?
Alexander the Great's conquests helped to bring Hellenisitc culture to the far reaches of the Mediterranean and beyound, which resulted in the broadening of ancient culture.
As Alexander and his armies moved across the world, they took with them the ideas and cultural heritage of their homeland. Alexander founded many Greek-style cities throughout the empire which became centers of Hellenistic learning and culture. He also absorbed new ideas into his army. When he conquered the Persian Empire he was quick to take many Persia administrators into his army. He also married a Persian woman and married several other Persian women to the men in his army.
Greek became the lingua franca of commerce thanks to his efforts at cultural inclusion, and after he died his generals set up Hellenistic Kingdoms which continued this cultural mixing until their incorperation into the Roman Empire.