The correct option is B the
In this statement, the writer says they have studied the 'history of America and Australia'. The noun here, 'history' is followed by the name of the countries. Hence the identity of the noun has been established by the following proper nouns, making 'the' the correct option to use before the specific noun 'history', and making Option A the correct answer. Option B cannot be used since the identity of the noun is already known to the writer as well as the reader. Option C is to be used before nouns that begin with a vowel, and since history begins with a consonant, it's an incorrect option. Option D is used when the noun is a proper noun, or an uncountable noun. In the given statement, history is a singular specific noun, making option D incorrect.