Learn French: Le stagiaire veut la prime, mais je doute que le chef la lui ait donnée. - The intern wants the bonus, but I doubt the boss gave it to him.

The phrase je doute que (I doubt that) expresses uncertainty and triggers the subjunctive mood. Because the action of giving the bonus happened before the doubting, we need the past subjunctive (subjonctif passé). It is formed using the present subjunctive of the auxiliary avoir (ait) and the past participle (donnée).

Why does donnée have an extra e at the end even though it uses the auxiliary verb avoir?

In compound tenses formed with avoir, the past participle must agree with the direct object if that object comes before the verb. Here, the preceding direct object is the pronoun la (referring to the feminine noun la prime), so we add an e to make donnée feminine.

Why are the pronouns in the order la lui?

When a sentence has two third-person object pronouns, the direct object (la, replacing la prime) always comes before the indirect object (lui, replacing au stagiaire). If the indirect object were first- or second-person (like me or te), it would come before the direct object.

Is stagiaire a masculine or feminine noun?