他教她日语，她教他英语。

He teaches her Japanese in exchange for she teaching him English.

李雷要吉姆教他英语。

Li Lei asks Jim to teach him English.

他教她法语， 她教他英语， 互教互学（作为交换条件）。

He's giving her French lessons in exchange for (ie as an exchange for) her teaching him English.