Learn Portuguese (Portugal): Precisamos de resolver o que aconteceu ontem. - We need to resolve what happened yesterday.

When "what" means "the thing that" in the middle of a sentence, you must use the free relative pronoun o que. If you only used que, it would just mean "that" (like a connecting word), which wouldn't make sense here.

Could I use aquilo que instead of o que?

Yes! You can absolutely say Precisamos de resolver aquilo que aconteceu ontem. Both mean "what" or "the thing that" and act as free relative pronouns. o que is just the shorter and more common choice in everyday spoken Portuguese.

Why do we need de after Precisamos? Doesn't resolver already mean "to resolve"?

The verb precisar (to need) requires the preposition de whenever it is followed by a noun or an infinitive verb. Even though resolver gives you the "to" in English, you must always use the structure precisar de to mean "to need to do something".

Why is the verb aconteceu in the past tense here?

It is the simple past tense (Pretérito Perfeito) of the verb acontecer (to happen), conjugated for the "it" form. Because the action was a single event that finished ontem (yesterday), we use this completed past tense.