Mrs. Nguyen explained to the class that they did well on their achievement exams. Option B is correct.
"Well" is the best option to fill the blank due to the fact that it is an adverb and those type of words are intended to modify verbs. In this particular case. the "word" well is describing the performance in the exams. In other words, well is modifying the verb "did."
The adverb "well" is defined by the dictionary as "in a good or satisfactory way" and "in a thorough manner."