What did Alexander do to unite the Macedonian and Persian cultures?

Answer 1

When he became king, he already owned Macedonia and Greece. When he conquered Persia, he crowned himself king of Persia as well. As any people will do when occupied, the Persians gradually became more and more Macedonian, (a Greek culture) using phalanx-capable soldiers, speaking and writing Greek, using Greek names, ect. In this way, he united the Macedonian and Persian cultures.

Answer 2

Cities under Alexander's rule flourished without fear of attack. This protected and promoted trade which lead to the emergence of primary routes like the Silk Road. Along the silk road Hellenic civilization, language and culture were spread and fused with local culture influencing religion (Buddhism, Judaism, Christianity), art, science and philosophical ideas . These Hellenized cultures too were spread by missionaries and traders (now able to communicate with the Greek lingua franca) and continued for hundreds of years after Alexander's death until new empires emerged and fused Hellenism with their own culture spreading the Greek civilization further still, impacting the whole world to the present day.

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He hoped that he could introduce Greek culture into the ex-Persian Empire which was now his own empire. It affected only the upper class, so the mainstream people continued on in their normal ways. His early death precluded him from taking this further, so we don't know how successful it might have been. The eastern areas soon reverted to their old cultures, or were over-run with invading peoples.