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:
- **West Africa and China**: While China is considered a classical civilization, West Africa is typically classified under later societies or empires.
- **Mesopotamia and Greece**: Mesopotamia is considered a river valley civilization, but Greece is classified as a classical civilization.
- **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.