The correct option is B that she was cheating on me - apposition to the noun
When a noun or its equivalent is in apposition to another noun/its
equivalent, its sole purpose is to provide extra information about that
noun/equivalent. For example: Barney, the dinosaur, is purple. Here the
noun in apposition is a noun phrase, 'the dinosaur' that gives
information about the noun 'Barney'. The noun/its equivalent in
apposition immediately follows the noun it qualifies.
Option C is correct because "that she was cheating on me" is a noun clause (it begins with a relative pronoun, 'that' and functions as a noun). It gives more information about the noun (the subject here) "fact".
Option A is incorrect because it does not include the noun clause at all; it includes the entire sentence excluding the noun clause in question. Moreover, it is not the subject.
Option B is incorrect because it is a phrase, it isn't a noun clause; it does not contain a subject nor verb.
Option D is incorrect because "to believe" is a phrase, not a clause or a noun clause.