Azáltal, hogy elolvassuk a hibajegyzéket, megtaláljuk a kipufogó hibáját.

It is a fixed expression meaning something like by doing X, through the fact that X, or by means of X happening.

So in this sentence, azáltal, hogy elolvassuk a hibajegyzéket introduces the method: we achieve the result by reading the error list.

A very literal breakdown is:

• azáltal = thereby / by that means
• hogy = introduces the clause, roughly that

But in natural English, the whole phrase is usually best translated as by + -ing.

Because in this meaning it functions as a single adverbial word: thereby / by that means.

Hungarian also has cases where az and által can appear separately, but azáltal as one word is the normal form in the expression azáltal, hogy.

So learners should usually treat azáltal, hogy as one chunk.

There are two reasons:

1. Hungarian normally uses a comma before a subordinate clause introduced by hogy.

   • so: azáltal, hogy...

2. The whole hogy-clause comes before the main clause, so another comma marks where that clause ends.

   • Azáltal, hogy elolvassuk a hibajegyzéket, megtaláljuk...

So the commas are not optional here in standard writing.

The prefix el- often gives the idea of completion.

• olvas = read
• elolvas = read through, finish reading

So elolvassuk a hibajegyzéket suggests we read the error list through / we read it completely, not just we are reading it in a general sense.

That fits the logic of the sentence: first the list is fully read, then the fault is found.

The prefix meg- often marks a completed result.

• talál = find, come across
• megtalál = successfully find, locate

In many English translations, both may simply appear as find, but in Hungarian meg- helps show that the action reaches its endpoint.

So megtaláljuk emphasizes the result: we find it / we succeed in finding it.

Because both verbs are in the definite conjugation.

Hungarian verbs are conjugated differently depending on whether the direct object is indefinite or definite.

Here both objects are definite:

• a hibajegyzéket = the error list
• a kipufogó hibáját = the exhaust's fault / the fault of the exhaust

So Hungarian uses the definite verb forms:

• elolvassuk
• megtaláljuk

A useful comparison:

• olvasunk egy könyvet = we are reading a book
• olvassuk a könyvet = we are reading the book

Also, in elolvassuk, the spelling reflects sound changes: olvas + juk does not stay olvasjuk. The s and j merge, giving ss: olvassuk.

Because it is the accusative form, marking the direct object.

The base word is hibajegyzék.
To make it the object of the verb, Hungarian adds the accusative ending -t. Often that ending appears with a linking vowel, so instead of just -t, you get forms like -ot, -et, -at, -öt.

Here:

• hibajegyzék → hibajegyzéket

So a hibajegyzéket means the error list as the thing being read.

It is a compound noun:

• hiba = error, fault
• jegyzék = list, register

So hibajegyzék is literally error-list.

Hungarian forms compounds very freely, and they are often written as one word, just as here.

This is a possessive structure.

• kipufogó = exhaust
• hiba = fault
• hibája = its fault
• hibáját = its fault, as a direct object

So a kipufogó hibáját is literally something like the exhaust its fault.

That is a normal Hungarian way to express possession:

• possessor first: a kipufogó
• possessed thing with possessive suffix: hibáját

Hungarian does not always need an of-phrase like English does.

Because several pieces are stacked together:

1. base noun: hiba = fault
2. possessed form: hibája = its fault
3. accusative form: hibáját = its fault, as object

The -ja is the 3rd-person singular possessive ending here.
Then the accusative -t is added after that.

So this is the order:

hiba → hibája → hibáját

That is why the form looks longer than the English word fault.

Yes. Hungarian can mark the possessor explicitly:

• a kipufogó hibáját
• a kipufogónak a hibáját

Both can mean the exhaust's fault.

The version without -nak/-nek is very common and neutral.
The version with kipufogónak can sound a bit more explicit or emphatic, depending on context.

It is not completely fixed. Hungarian word order is flexible and often shows emphasis.

The given sentence starts with the method:

• Azáltal, hogy elolvassuk a hibajegyzéket, ...

This foregrounds how the result is achieved.

You could also say:

• Megtaláljuk a kipufogó hibáját azáltal, hogy elolvassuk a hibajegyzéket.

That is still grammatical, but the emphasis shifts.

A very natural alternative is:

• A hibajegyzék elolvasásával megtaláljuk a kipufogó hibáját.

This expresses roughly the same idea using a different structure.

Not necessarily.

Hungarian, like English, often uses we in explanations, instructions, and technical descriptions in a general way. It can mean something like:

• this is how we do it
• this is how one finds it
• this is how it is found

So depending on context, the sentence may describe a real we, or it may be using a more general instructional style.