Final answer:
The sentence should be written as 'Even though Valerie did nothing wrong, she felt extremely guilty.'
Step-by-step explanation:
The best way to write the sentence is option C: Even though Valerie did nothing wrong, she felt extremely guilty. This sentence follows proper comma usage. The subordinate clause 'Even though Valerie did nothing wrong' is followed by a comma before the main clause 'she felt extremely guilty.' This structure effectively conveys the cause-and-effect relationship between Valerie's lack of wrongdoing and her strong feelings of guilt.
Option A ('Even though Valerie did nothing wrong; she felt extremely guilty') incorrectly uses a semicolon, which is not appropriate for joining two independent clauses. Option B ('Valerie felt extremely guilty, even though she did nothing wrong') places the adverbial clause 'even though she did nothing wrong' after the main clause, which disrupts the logical flow of the sentence. Option D ('Valerie felt extremely guilty; even though Valerie did nothing wrong') unnecessarily repeats the subject and is not grammatically correct.
Therefore, option C is the best choice for correctly and clearly expressing the intended meaning of the sentence.