Step 1: Understanding the question.
The sentence describes how the person faced life's challenges, and we need to choose a word that reflects the calmness and composure with which they handled these challenges.
Step 2: Analyzing the options.
(A) equanimity: This is the correct choice, as "equanimity" means mental calmness, composure, and evenness of temper, especially in difficult situations. It fits perfectly with the context.
(B) tranquility: While "tranquility" refers to calmness, it does not imply the ability to handle challenges, as equanimity does.
(C) silence: This word does not fit, as it refers to the absence of sound, not the ability to face challenges.
(D) peace: "Peace" is too general and does not specifically imply composure in the face of challenges.
Step 3: Conclusion.
The correct answer is (A) equanimity, as it best describes the composure with which the person faced difficulties.