明白

彼の才能は誰の目にも ___ である。

The correct answer is 「明白」(めいはく), meaning "clear," "obvious," or "evident." When someone's talent is 明白, it means it is easily seen and understood by everyone, as indicated by "誰の目にも" (in everyone's eyes). 「巧妙」(こうみょう) means "skillful," "clever," or "ingenious"; while talent can be skillful, 巧妙 implies a hidden cleverness, not something clearly visible to everyone. 「密か」(ひそか) means "secret" or "private"; a talent that is 密か would not be apparent to everyone. 「愚か」(おろか) means "foolish" or "stupid"; this is clearly incorrect as it describes a negative quality, not talent.

正解は「明白（めいはく）」です。「誰の目にも」という表現と合わせて、彼の才能が「誰が見てもはっきりしている」という意味に最も合います。「巧妙」は巧みであること、「密か」はこっそりしていること、「愚か」は愚かなことを意味し、文脈に合いません。