What are the four ancient civilizations?

Ancient Mesopotamia, Egypt, Greece, and Rome.

There are actually 4 cradles of civilization:

Ancient Mesopotamia, ancient Egypt, Ancient India (Indus Valley, and the near Aryan Age), and Ancient China.

Following that came the 2 European civilizations of Ancient Greece, and ancient Rome.

After that came the Mayans, Aztecs, and the new patterns of civilization.

My Source: World History: The Human Odyssey, by Professor Jackson J. Spielvogel.

I recommend you to read the book for a more thorough answer.