averiguarían
-they would find out
The word averiguarían is the conditional form of averiguar in the third person plural.
See the full averiguar conjugation

averiguar

Y él me prometió que ustedes lo averiguarían al final.
And he promised me that you'd figure that out in the end.
¡De esa manera nunca averiguarían que él robo la corona!
That way you'll never find out that he stole the crown!
Y él me prometió... Que ustedes lo averiguarían al final.
And he promised me... that you'd figure that out in the end.
¿Cómo iba a saber que ellos lo averiguarían?
What did I know he will find out?
Sabía que lo averiguarían, así que...
I knew you'd find out, so...
Y averiguarían que eres una fugitiva y tendrían que llamar a la policía
Then they'd find out you a fugitive and they'd have to call the police.
Te dije que lo averiguarían.
I told you they'd figure it out.
¿Crees que han estado robando pólvora y que los alemanes no averiguarían adónde iba?
They've been stealing and they aren't going to find out where it was going?
Sabía que lo averiguarían.
Shucks, I knew they'd find out.
Si se lo decía a la policía averiguarían que a Dante le pagaron por perder la vez pasada.
If I told the police... they would've found out that Dante took a fall the last time.
En un llamado a la oficina del procurador de Djizak, su asistente respondió que averiguarían qué estaba ocurriendo.
In a phone call to the Djizak prosecutor's office, the prosecutor's assistant answered that they would find out what is happening.
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