Answer:
B. He
Step-by-step explanation:
In the sentence, what is missing is a subject or a subject pronoun, that is to say, someone or something that does the main action "went"
Subject pronouns are I, we, they, you, he, she and it. So, from all given choices, the "He" pronoun is the one that correctly completes the sentence: "My classmates and he" are the subjects, the ones that performed the main action of going to the science museum to see the new exhibit.
The other options are incorrect because "them", "him" and "her" are all object pronouns, that is to say, pronouns that are affected by the action of the subject, or are the object of a preposition, they do not function as subjects.