Learn Hardcore Russian: В гараже стоит машина моего брата.

Because it describes location (where), not motion (to where). In Russian, в + Prepositional answers где? (where): в гараже. If you mean movement into the garage, you use в + Accusative answering куда? (to where): в гараж.

What does стоит mean here? Why not just “is”?

Стоит is the 3rd person singular of стоять “to stand.” Russian often specifies an object’s position: cars and other upright objects typically стоят (stand), books on a shelf often лежат (lie), pictures висят (hang). Here стоит means “is (standing/parked).” You could also say находится (“is located,” more neutral/formal) or припаркована (“is parked,” participle).

Why is it моего брата? What case is that?

It’s the Genitive case to show possession: машина моего брата = “the car of my brother.” Both words are in the Genitive: моего (Genitive masculine/neuter of мой) + брата (Genitive singular of брат).

Why not моей брата?

Because брат is masculine. In the Genitive:

masculine/neuter: моего
feminine: моей
plural: моих

So with брата (masculine), you must use моего.

Could I say Машина моего брата стоит в гараже instead? Does word order matter?

Yes, that’s perfectly correct. Russian word order is flexible and is used to highlight information. The original sentence front-loads в гараже to emphasize the place (e.g., as an answer to Где…?). Машина моего брата стоит в гараже is more neutral.

Can I drop the verb and say В гараже машина моего брата?

Yes, in colloquial speech and especially in answers, the verb can be omitted: В гараже машина моего брата. It sounds like a terse statement of location. Adding есть is usually unnecessary here; В гараже есть машина моего брата would emphasize existence more than location.

Is стоит ambiguous with “costs”?

On its own, стоит can mean “stands” or “costs.” Context resolves it:

Location: Машина моего брата стоит в гараже = is (standing) in the garage.
Price: Машина моего брата стоит два миллиона = costs two million.

How do I pronounce the tricky parts?

стоИт (stress on И).
в гаражЕ (stress on the last syllable).
машИна (stress on И).
моегО (stress on the last syllable; in endings -ого/-его, the written г is pronounced like в: моего ≈ “ma-ye-VO”).
брАта (stress on the first syllable).

Why is гараже in that form? What case is it?

Гараже is Prepositional singular, required by в when indicating location. The base noun is гараж; in the Prepositional (locative) it becomes в гараже. Compare motion: в гараж (Accusative).

Could I use автомобиль instead of машина?

Yes: В гараже стоит автомобиль моего брата. Машина is the common everyday word; автомобиль is more formal/technical. Slang options like тачка exist but are informal.

Is моего modifying машина or брата?

Моего modifies брата. The whole Genitive phrase моего брата (“of my brother”) modifies машина. Agreement is within that phrase: моего (masc. gen.) matches брата (masc. gen.), not машина.

What tense/aspect is стоит, and how would other forms look?

Стоит is present tense, imperfective (ongoing state). Key forms with машина (feminine):

Past: машина стояла в гараже
Future: машина будет стоять в гараже
Perfective options exist (e.g., постоять, простоять) but they add nuances like “stand for a while/for a duration,” not usually needed for simple location.