Answer:
B. During the four days that we were on vacation, my dog refused to eat.
Explanation:
Generally, when you want something to be easier to understand, avoid repetitive information, and don't use passive voice. A passive voice indirectly refers to something, like "my homework has been completed", rather than "I've done my homework".
In this, there are 2 key pieces of information that should be clear in the answer:
They were on vacation.
The dog refused to eat.
A. is repetitive because it says that they were out of town on vacation- by being on vacation, it's implied that you're out of town (although there are some exceptions).
C. has the same problem as A, but concisely explains that the dog didn't eat.
D. has both of the problems of A, and seems like a word by word paraphrase of the original.
I hope this helps!