Answer: The right answer is the B) después de.
Explanation: Just to elaborate a little on the answer, it can be added that the adverb "después" means after, or later on. In this sentence, the speaker is saying that he/she "is going to the tailor __________ going to the laundromat," so the most appropriate option is after—"I am going to the tailor after going to the laundromat." The conjuntions "y" and "ni" mean and and nor, respectively, and they would not complete the sentence in a correct way. In addition, the adverb "entonces" means then, and it would not complete the sentence in a correct way, either.
