Learn Italian: Speravamo che avessi intercettato il codice. - We hoped that you had intercepted the code.

The main verb speravamo is in a past tense and expresses hope, which requires the subjunctive mood. Because the action of intercepting happened before the hoping, we must use the pluperfect subjunctive (trapassato congiuntivo) to show that chronological step back in time.

Since avessi can mean 'I' or 'you', how do we know this means 'you'?

The imperfect subjunctive forms for io and tu are both avessi. We translate it as 'you' here based on assumed context. If this were a real conversation and the context wasn't obvious, an Italian speaker would add the pronoun, saying che tu avessi intercettato to clear up any confusion.

Could we use the passato prossimo (abbiamo sperato) instead of the imperfetto (speravamo) for the main verb?

Yes, but it shifts the focus. Speravamo (we were hoping) describes an ongoing state of mind in the past, which is very common with verbs of feeling. Abbiamo sperato describes a completed, isolated instance of hoping. Both are past tenses, so both would still trigger the pluperfect subjunctive for an earlier action in the second part of the sentence.

Why does intercettato end in -o here, regardless of who intercepted the code?