The correct option is C that the students were inspired by her
An adverb clause is a group of words containing a subject and a verb, and it functions as an adverb, by modifying an adjective, verb or an adverb. Adverb clauses generally begin with a subordinate conjunction (since, because, while, etc.)
Option C is correct because it is an adverb clause of result or consequence, 'such...that' is a pair of conjunctions that refers to result: "that the students were inspired by her".
Option A is incorrect because it contains a coordinate/independent clause, whereas an adverb clause is subordinate/dependent.
Similarly, option B is incorrect as it contains a coordinate clause.
Option D is incorrect because the answer lies in C.