I actually believe the correct answer is an adverb clause modifying was.
A is incorrect because the first clause is subordinate; B is incorrect because there is no noun clause in this sentence; C is incorrect because the word modifying school is an adjective, but not an adjective clause; this leaves us with D. We can see the adverb clause 'when the Little Red Schoolhouse began to give way to the consolidated school in the 1920s' which modifies the verb 'was.'
