habían terminado

had finished

→ haber
phrase Rare #41,631
had finished Past perfect tense: they had completed something before another past event. In some contexts it can also mean they were finished with something.
SP: Cuando llegué, ellos ya habían terminado de comer.
EN: When I arrived, they had already finished eating.

Aquella tarde ella le dijo que habían terminado.

That afternoon she told him that they had broken up.

— It's Such a Beautiful Day (2012)

Para cuando llegué a casa ya se habían terminado la tarta.

By the time I got home, they had already finished the cake.

Creí que ustedes habían terminado.

I thought you guys were done.

Tom oyó que Mary y John habían terminado.

Tom heard that Mary and John had broken up.

Ya habían terminado el trabajo.

They had already finished the job.