(a) She don't like to play tennis. "She" is singular third-person, so it requires "doesn't." "Don't" is incorrect. Should be: "She doesn't like to play tennis." Incorrect.
(b) He doesn't likes to read books. "He" is singular third-person, so "doesn't" is correct, but the verb should be "like" (base form), not "likes." Should be: "He doesn't like to read books." Incorrect.
(c) They doesn't go to school on Sundays. "They" is plural, so it requires "don't," not "doesn't." Should be: "They don't go to school on Sundays." Incorrect.
(d) He doesn't like to read books. "He" is singular third-person, so "doesn't" is correct, and "like" is the correct base verb form. This sentence is grammatically correct. Correct.