Correct option is A
The word “while” is typically used to indicate two actions happening at the same time. However, in this sentence, “he saw the bear” happened first, and the other actions (running, dropping the gun, climbing) followed as a reaction. Therefore, “when” is the correct conjunction to show that one action happened and triggered the next.
Corrected Sentence:
"When he saw the bear, he ran to the nearest tree, dropped his gun and climbed to a safe place."