In Spanish you may omit the subject (in this case, ustedes) when the verb hints at it (sujeto tácito), so the commonly used form is the following:
¿Hicieron su tarea de hoy?
¿Hicieron su tarea para hoy??. Let me explain the difference with another example:
¿Construyeron el muro para María?
means to ask if the wall built was intended for María or not, while
¿Construyeron el muro de María?
means to ask if María's wall was indeed built.
With this in mind, you can now see that the alternative in gray is asking whether [they] did their homework intending it for today, rather than if [they] did today's homework or not.
In reality, both questions will be perfectly understood, it's just that one is not entirely correct.
Regarding your question about why
su tarea and not
The first part (
hicieron [ustedes]) is plural, but the direct object
su tarea is singular because
tarea is commonly used as a collective word (just as you don't say
Let me pose a different example for this:
- ¿Tienes tu llave? // Do you [one person] have your key?
- ¿Tienes tus llaves? // Do you [one person] have your keys?
^ Here it is clear that the individual subject is asked first for a single key and then for multiple keys.
- ¿Tienen su llave? // Do you [people] have your key?
^ Even with plural subject, it is clear that the question asks for everyone to have exactly one key (i.e., singular direct object).
- ¿Tienen sus llaves? // Do you [people] have your keys?
Please note that this last question is now (slightly) ambiguous in both languages. It could mean to ask for one single key per person (they collectively have keys), or it could mean that every individual might have multiple keys.
While this is not very surprising, analyzing this could help you understand the translation to Spanish.
As a last note, a teacher that left multiple assignments, who wants to clearly emphasize that fact could say:
¿Hicieron sus tareas?
Hope this helps :)