b. The new student in my class, who moved here from North Carolina, is very nice.
Explanation:
You use commas "," either to separate independent clauses- parts of a sentence that can be their own sentence- or to separate a dependent clause at the beginning of a sentence- a part of a sentence that can't be its own sentence.
In this case, the the beginning of the sentence, "The new student in my class," which cannot stand on its own as a sentence, must have a comma after it because that is one of the comma rules. It's a dependent clause because it does not have a complete thought. It doesn't say what "the new student in my class" is doing or what is happening to them.
