hubieran comido
Past perfect subjunctive ellos/ellas/ustedes conjugation of comer.

comer

Volvieron a la casa contentos y satisfechos de sí mismos casi como si ellos se hubieran comido el pastel y no tuvieron problema alguno para abrir la puerta.
They returned home happy and self-satisfied, almost as though they had eaten the cake themselves, and didn't have any trouble opening the door.
Word of the Day
to skate