Explanation
Correct answer: C.
Choice C is the best answer. "Eventually" logically signals that the information in this sentence—that textile artists will remove the cloth when it has turned red—is the final step in the chronological sequence of the dyeing process described in the previous sentences.
Why the other choices are wrong
Choice A
Choice A is incorrect because "nevertheless" illogically signals that the information in this sentence is true despite the previous information about simmering the cloth in the dyebath. Instead, the removal of the cloth is the final step in the dyeing process.
Choice B
Choice B is incorrect because "likewise" illogically signals that the information in this sentence is similar to the previous information about simmering the cloth in the dyebath. Instead, the removal of the cloth is the final step in the dyeing process.
Choice D
Choice D is incorrect because "in other words" illogically signals that the information in this sentence is a paraphrase or restatement of the previous information about simmering the cloth in the dyebath. Instead, the removal of the cloth is the final step in the dyeing process.