Apenas hube cerrado el libro, recordé la respuesta.
Barely had I closed the book when I remembered the answer.
The first action was completed, and immediately the second one appeared. Therefore, the form hube cerrado fits the meaning.
En cuanto hubiste escuchado la noticia, cambiaste de opinión.
As soon as you had heard the news, you changed your opinion.
Here Pretérito Anterior emphasizes that the change of opinion happened after receiving the information.
Tan pronto como hubo terminado el discurso, el público aplaudió.
As soon as he had finished the speech, the audience applauded.
The applause began immediately after the end of the speech. This is a typical situation for this tense.
Cuando hubimos cruzado el puente, vimos la ciudad.
When we had crossed the bridge, we saw the city.
First, the crossing of the bridge was completed, then a new event appeared — the people saw the city.
Después de que hubieron explicado las condiciones, los clientes aceptaron.
After they had explained the conditions, the clients agreed.
Here the order of actions is important: the explanation ended before the clients’ agreement.
In everyday speech, all these sentences can be simplified. For example, instead of cuando hubimos cruzado, one can say cuando cruzamos. That will be normal for conversation. But in a text, especially a literary or historical one, Pretérito Anterior helps make the sequence more expressive.
The main thing to remember is this: Pretérito Anterior is not a basic conversational tense. It should not be used in every phrase about the past. It is needed for the precise description of an action that was completed immediately before another past event. If you read Spanish books, documents, or classic texts, knowing this form will help you better understand the author’s style and the order of events.