Explanation
Correct answer: C.
Choice C is the best answer. "For example" logically signals that this sentence supports the previous information about the descriptive notations opera singers use by providing specific examples of these notations: giocoso (playfully) and lento (at a slow tempo).
Why the other choices are wrong
Choice A
Choice A is incorrect because "on the other hand" illogically signals that the information in this sentence contrasts with the previous information about the descriptive notations opera singers use. Instead, the sentence provides examples of these notations.
Choice B
Choice B is incorrect because "all the same" illogically signals that the information in this sentence is true despite the previous information about the descriptive notations opera singers use. Instead, the sentence provides examples of these notations.
Choice D
Choice D is incorrect because "in the second place" illogically signals that the information in this sentence is a second point that is separate from the previous information about the descriptive notations opera singers use. Instead, the sentence provides examples of these notations.