有 / 没有 + 能力 + [verb phrase]
[noun] + 能力 + 强 / 弱
学 / 有 + 本领
发挥 / 表现出 + 才能
能力, 本领 and 才能 all name what someone is able to do. 能力 is general capacity, 本领 is a practical skill you have learned, and 才能 is talent that shows in what you produce.
能力 is the neutral, measurable word. It takes 强 and 弱, combines with a field before it – 学习能力, 语言能力 – and can take a verb phrase after 有: 有能力做 "be capable of doing".
本领 is a skill you acquire by practice: fixing things, swimming, surviving. It goes with 学, 有 and 大, and sounds more concrete and spoken than 能力. It doesn't combine with a field word the way 能力 does.
才能 is a gift that shows in art, leadership or organising. It goes with 发挥 "bring into play" and 表现出 "display", and rarely with 强.
才能 also appears as two words: 才 "only then" plus 能 "can". That one sits before a verb; the noun sits where a noun does. The pinyin is the same.