Domi tacemus, ut aviam audire possimus.

Domi means at home. It’s the locative form of domus (home/house) and is a standard Latin way to express location at home without a preposition.
You can say in domo, but that more literally means in the house (more physical/inside-the-building), while domi is the idiomatic “at home.”

Tacemus is 1st person plural, present, indicative, active of tacēre (to be silent).
The subject we is built into the verb ending -mus, so Latin doesn’t need an explicit pronoun here.

Because ut aviam audire possimus is a subordinate clause (a purpose clause) introduced by ut. Latin often separates such clauses with a comma, especially in modern edited texts, to make the structure clearer.

Here ut means so that / in order that and introduces a purpose clause.
A big clue is that the verb in the ut-clause is subjunctive (possimus). Purpose clauses are typically ut + subjunctive (or nē + subjunctive for negative purpose).

Because it’s inside a purpose clause. Latin uses the subjunctive mood after ut to mark intention/purpose:

• Main clause: we are silent
• Purpose: so that we may be able to hear… → possimus (present subjunctive)

If you used possumus, it would read more like a straightforward statement (we are able) rather than a purpose construction.

The present subjunctive in a purpose clause is normal when the main verb is present (or when the idea is general/habitual):
We keep quiet (now / generally) so that we can hear…
It reflects a purpose seen as contemporaneous with the main action.

Aviam is accusative singular of avia (grandmother). It’s accusative because it is the direct object of audīre (to hear):
to hear (whom?) grandmother → aviam

Possumus/possimus commonly takes an infinitive to complete its meaning:

• posse = to be able
• audīre = to hear
  So audire possimus = we may be able to hear.

Here, audīre is a complementary infinitive dependent on possimus.

It could. The difference is nuance:

• ut aviam audiamus = so that we may hear grandmother (focus on the hearing itself)
• ut aviam audire possimus = so that we may be able to hear grandmother (focus on having the opportunity/ability—e.g., because it’s quiet enough)

Latin often uses posse + infinitive when ability/opportunity is part of the idea.

Yes, but it’s flexible. A common pattern is:

• ut
  • (object) + (infinitive) + (subjunctive verb)

Putting aviam early makes it prominent: grandmother is what matters most to hear. Ending the clause with possimus is also typical, since Latin often places the finite verb late.

Negative purpose uses nē instead of ut:

• Domi tacemus, nē aviam audire possimus.
  = At home we are silent, so that we may not be able to hear grandmother.

If you meant “so that we don’t hear (even though we could),” you’d more likely write:

• Domi tacemus, nē aviam audiāmus.
  = …so that we don’t hear grandmother.

Either is possible with the present tense. Context decides:

• right now: We’re being quiet at home…
• habitual/general: At home we keep quiet…

Latin present indicative often covers both current and general present ideas.