Which of the following sentences is grammatically correct?

The sentence "She doesn’t like ice cream" is grammatically correct due to the proper use of the auxiliary verb "does" in contraction form with "not." In English, when using "does" for third-person singular subjects (he, she, it), the verb that follows should be in its base form, which is "like" in this case.

The structure "does not" allows the speaker to express the negative without changing the verb form. Therefore, "doesn't" + "like" effectively conveys that she has a dislike for ice cream. This adherence to subject-verb agreement and the correct form of negation confirms the correctness of the sentence.

Other options vary in grammatical structure. Using "don’t" is incorrect with a third-person singular subject, and "doesn't likes" mistakenly combines the auxiliary with an incorrect verb form. The phrase "She not likes" also contains a grammatical error, as it improperly omits the auxiliary verb needed for negation.