Read the French literally and the answer appears. "Raison" is reason, "de" is of, and "etre" is the verb to be, the same word behind English words like essence. So the phrase is "reason of being". The one thing to be careful about is which sense of "reason" is meant. Here it means purpose or justification, not logic or argument, and three of the four options are built to exploit exactly that slip.
An easy test: try swapping the option into a real sentence. "Fighting hunger is the raison d'etre of this organisation" makes sense only if the phrase means the reason the organisation exists. Option (B) is the answer.
Let's summarize:
The correct option is (B), reason for existence.
LIST I | LIST II (Meaning) | ||
| A | Break into | I | in search of |
| B | Cut down | II | wear |
| C | Look out for | III | enter by force |
| D | Put on | IV | reduce |