The correct answer is: Anil met an American and a European man yesterday.
The indefinite article “an” is used before singular nouns that refer to a general or unspecified person or thing. In this case, Anil met two men, one from America and one from Europe. We do not know the names of the men, so we use the indefinite article “an” before each nationality.
The definite article “the” is used before singular nouns that refer to a specific person or thing that has already been mentioned or is known to the reader or listener. In this case, Anil has not mentioned the names of the men, so we cannot use the definite article “the” before either nationality.
The article “a” is used before singular nouns that refer to a general or unspecified person or thing. However, it is not used before nationalities.
The article “no article” is used before singular nouns that refer to a general or unspecified person or thing. In this case, Anil met two men, one from America and one from Europe. We do not know the names of the men, so we do not use any article before either nationality.