D. Jimmie's and Sarah's.
A is not the correct answer because "Jimmies" and "Sarahs" only tell us that there is more than one Jimmie and Sarah. It does not give us the singular possessive.
B is not the correct answer because it simply makes no grammatical sense. You cannot place an "'s" next to only one name if there are two names.
Try deleting the "and", splitting up, and rearranging the sentence...
---> Jimmie birthday is two days apart from Sarah's. (incorrect)
---> Sarah's birthday is two days apart from Jimmie's. (correct)
C is not the correct answer because, like option B, it makes no grammatical sense.
I hope this helps a lot! :)
