Step 1: Understand the meaning of PUISSANT.
Puissant is an adjective meaning having great power, strength, or influence; mighty. It is commonly used for rulers, armies, or nations that command great force, as in "a puissant king" or "a puissant army."
Step 2: Match it with the closest option.
Powerful directly captures the idea of possessing great strength or authority, which is exactly what puissant conveys.
Step 3: Eliminate the other options.
Skillful refers to being proficient or expert at something, not to raw strength. Colorful and Beautiful both describe visual or aesthetic appeal, which has nothing to do with power. Gainful relates to earning profit or wages, an entirely different idea.
Step 4: Conclusion.
Powerful, option (a), is the correct synonym of puissant.