(NB. I speak Australian English, so my knowledge uses British English as its basis; e.g. "A colourful theatre programme.")
To me, D is the correct answer. It's saying "he has no car." B has included "does" which my awful memory knows is often used as an auxiliary verb. For instance, "I paint the wall" can become "I did paint the wall" instead of "I painted the wall."
My Grade Four teacher back in the 1970s disliked the use of "got" (and "gotten" was dismissed as An American Word, meaning, "it's just wrong and that's all there is to it!") when it has no real purpose in a sentence. As a word meaning "get" in a past tense, that's absolutely fine. But in a sentence like "I've got three pencils", -- that is, I possess three pencils -- 'got' isn't needed. "I have three pencils" is, I think, preferable. Except if the sentence were in response to "how many pencils did you get from the office?"
Sorry, I'm being long-winded. Answer B is not a correct sentence, the "got' is not required. Except if the sentence were asking "did he get a car yesterday, from a car yard?" In which case B would read "he didn't get a car" or "he hasn't got a car."
I hope this makes sense, sorry for any further confusion I might have caused you.