気さく

彼は ___ な性格で、誰とでもすぐに打ち解ける。

The correct answer is 「気さく」(きさく), meaning "friendly," "sociable," or "easy-going." This personality trait explains why he "誰とでもすぐに打ち解ける" (gets along with anyone quickly). 「気まぐれ」(きまぐれ) means "whimsical" or "fickle"; a whimsical person might be unpredictable, not necessarily someone who quickly befriends everyone. 「気丈」(きじょう) means "resolute" or "strong-willed" (especially in the face of adversity); this doesn't directly relate to easily socializing. 「気弱」(きよわ) means "timid" or "faint-hearted"; a timid person would likely find it difficult to quickly open up to others.

正解は「気さく（きさく）」です。「誰とでもすぐに打ち解ける」という説明に合うのは、「親しみやすく、気軽に話せる性格」を意味する「気さく」です。「気まぐれ」は気分屋であること、「気丈」は困難に強く耐えること、「気弱」は気が弱いことを意味し、文脈に合いません。