Final answer:
The sentence with correct capitalization is 'My aunt couldn't help me with my homework because she never took American history in high school.' Proper nouns and adjectives are capitalized, while common nouns are not.
Step-by-step explanation:
The sentence that uses capital letters correctly is: My aunt couldn't help me with my homework because she never took American history in high school. This sentence adheres to proper capitalization rules because 'American' is capitalized as it is a proper adjective, and 'history' is not capitalized as it is not part of a specific course title. 'High school' is not capitalized because it is a common noun, not part of a proper noun.