The correct option is B Without
The giant panda was lucky, because he did not get hurt by the storm.
To fill in the blank, we need a preposition that puts through the above message.
Option B: 'Without' means 'an action that did not happen'. It relates here, as it refers to the action of 'not getting hurt'. Hence option B is correct.
Option A: 'Outside' means 'situated beyond a limit or boundary', like the walls of a house.
The meaning does not relate here.
Option C: 'About' indicates 'movement within a particular area'.
Option D: 'Beyond' means 'outside the physical range of'.
These words do not form a complete meaning, they do not focus on why he was lucky, because he did not get hurt (without getting hurt).
Hence options A, C and D are incorrect.