Azáltal, hogy átvizsgáljuk a fényszórót, megértjük, miért bukott meg az autó.

Azáltal, hogy is a set expression meaning by doing something, through the fact that, or as a result of doing something.

So in this sentence, Azáltal, hogy átvizsgáljuk a fényszórót means something like:

• By inspecting the headlight
• Through inspecting the headlight

Literally, azáltal is roughly by that / through that, but in natural English you usually would not translate it word-for-word.

Because Hungarian normally uses azáltal, hogy + full clause.

The part after it is not a noun phrase, but a whole clause with a finite verb:

• átvizsgáljuk a fényszórót = we inspect the headlight

So Hungarian connects it with hogy.

A useful pattern is:

• azáltal, hogy + clause = by doing X / through doing X

This is different from English, where by inspecting uses a gerund. Hungarian usually prefers a full clause here rather than an -ing-style form.

Átvizsgáljuk comes from átvizsgál = to inspect thoroughly / to examine carefully.

Parts:

• vizsgál = examine, inspect
• át- = across, through, thoroughly
• -juk = we with a definite object

So átvizsgáljuk means we inspect it thoroughly or we examine it carefully.

The prefix át- often gives a sense of going through something completely.

Because the verb is in the definite conjugation.

The direct object is a fényszórót = the headlight, which is definite. In Hungarian, when the object is definite, the verb often takes definite endings.

Compare:

• vizsgálunk egy fényszórót = we are inspecting a headlight
  indefinite object
• vizsgáljuk a fényszórót = we are inspecting the headlight
  definite object

So átvizsgáljuk is used because the object is a specific, definite thing.

Because it is the direct object of átvizsgáljuk.

Hungarian marks direct objects with the accusative suffix -t.

• a fényszóró = the headlight
• a fényszórót = the headlight as a direct object

So:

• átvizsgáljuk a fényszórót = we inspect the headlight

Megértjük means we understand.

It comes from:

• ért or érteni = understand
• megérteni = to understand, to grasp fully
• megértjük = we understand it / we understand

It uses the definite conjugation because what is being understood is a specific content clause:

• miért bukott meg az autó = why the car failed

In Hungarian, whole subordinate clauses can behave like definite objects, so definite verb forms are normal here.

Compare:

• Értjük. = We understand it.
• Megértjük, miért bukott meg az autó. = We understand why the car failed.

This is a very important Hungarian word-order point.

The basic verb is megbukik = to fail.

In a neutral statement, you often get:

• Az autó megbukott. = The car failed.

But when a question word such as miért = why comes before the verb, the verbal prefix usually moves after the verb:

• Miért bukott meg az autó? = Why did the car fail?

So in your sentence:

• miért bukott meg az autó

the prefix meg is after bukott because miért is in focus before the verb.

Yes. Here megbukott az autó means the car failed, usually in the sense of failing a test, inspection, or exam-like evaluation.

Hungarian uses megbukik not only for people failing exams, but also for things failing inspections or tests.

So if the context is a vehicle inspection, az autó megbukott means the car did not pass inspection.

Because az autó is the subject of bukott meg.

In the clause:

• miért bukott meg az autó

the meaning is why the car failed.

The car is the thing doing the failing, grammatically speaking, so it is the subject, not the object.

That is why it stays:

• az autó
  not
• az autót

Hungarian usually separates subordinate clauses with commas.

Here the opening part is a subordinate clause introduced by azáltal, hogy:

• Azáltal, hogy átvizsgáljuk a fényszórót, ...

Then comes the main clause:

• megértjük, miért bukott meg az autó

So the commas help show the clause boundaries:

1. after azáltal
2. after fényszórót

This is normal Hungarian punctuation with this kind of structure.

Hungarian often uses the simple present to express a general result, an immediate consequence, or an instruction-like statement.

So:

• Azáltal, hogy átvizsgáljuk a fényszórót, megértjük...

can mean something like:

• By inspecting the headlight, we understand...
• If we inspect the headlight, we will understand...
• Inspecting the headlight lets us understand...

The exact English tense depends on context, but Hungarian does not always need a future form where English might use one.

It is grammatical and clear, but it sounds a little formal or explanatory.

Some natural alternatives might be:

• Ha átvizsgáljuk a fényszórót, megértjük, miért bukott meg az autó.
  If we inspect the headlight, we understand / will understand why the car failed.

• A fényszóró átvizsgálásával megértjük, miért bukott meg az autó.
  By inspecting the headlight, we understand why the car failed.

The original sentence is perfectly acceptable, but azáltal, hogy is a somewhat more formal way to express the idea.