As far I know, "He ran down the stairs" is true. But I don't have any idea about the options suggested in this question. I was wondering if I could learn something from the teachers in this froum.
Your multiple choice question looks like homework and as a rule we don't do that here. We generally expect people to offer their own answers to such questions first.
Downstairs is used in sentences like these: He ran downstairs. He is downstairs. He came from downstairs.
As you say, down the stairs is also correct in many sit