The correct answer is D, 有时
The sentence translated into English is "On Saturdays, I sometimes play badminton, ______ plays table tennis."
The statement should be stating how frequently "I" play table tennis, so, the answer in the blank should be an adverb of frequency. From the above choices, A, 每, means "every", B, 都, means "also", C, 一起, meaning "together" and D, 有时, means "sometimes".
Only choice D is an adverb of frequency, "sometimes", therefore is the only choice that fits into the sentence.
