The phrase, 'work out' means 'resolve'.As this phrase conveys a clear meaning when used in the given sentence, option A is correct.
The phrase, 'work in' means 'to try to include something'. Eg: I have worked in a few tips in the new recipe that I have written down.
The phrase, 'work on' means 'to spend time producing or improving something'. Eg: Since he has started working on an urgent project, he does not have time to attend any party.
The phrase, 'work up' means 'to develop or improve something with some effort'. Eg: As I had a heavy breakfast, I can't work up any appetite for lunch.
Given the meanings as above, the phrases given in options B, C and D cannot be used in the blank to form a meaningful sentence. Hence, these options are incorrect.