Explanation
Correct answer: C.
Choice C is the best answer. The convention being tested is the coordination of main clauses within a sentence. This choice correctly uses a comma and the coordinating conjunction "and" to join the first main clause ("In 1919 Larrazolo was elected governor of New Mexico") and the second main clause ("in 1928 he became the nation’s first Hispanic US Senator").
Why the other choices are wrong
Choice A
Choice A is incorrect because when coordinating two longer main clauses such as these, it’s conventional to use a comma before the coordinating conjunction.
Choice B
Choice B is incorrect because it results in a comma splice. Without a conjunction following it, a comma can’t be used in this way to join two main clauses.
Choice D
Choice D is incorrect because it results in a run-on sentence. The two main clauses are fused without punctuation and/or a conjunction.