The correct identification of civilizations with their classifications is:
Greece and Rome are classical civilizations.
Here is a brief overview of the classifications for the other options:
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West Africa and China: While China is considered a classical civilization, West Africa is typically classified under later societies or empires.
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Mesopotamia and Greece: Mesopotamia is considered a river valley civilization, but Greece is classified as a classical civilization.
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Egypt and Indus: Egypt is a river valley civilization, and the Indus Valley civilization is also classified as a river valley civilization, not classical.
So the only entirely correct pairing among the options provided is Greece and Rome as classical civilizations.