The sentence with correct pronoun-antecedent agreement is:
Mrs. Smith was excited to teach her class.
In this sentence, "her" correctly refers to the antecedent "Mrs. Smith."
The other sentences contain errors in pronoun-antecedent agreement:
- The twins laughing so hard should use "they" instead of "she."
- "Raindrops" is plural, so it should use "they" instead of "it."
- "The brothers" is plural, so it should use "they" instead of "he."