Azáltal, hogy megmérjük a profilmélységet, megtaláljuk a hibát.

Azáltal, hogy is a common Hungarian structure meaning by doing something, through the fact that, or by means of the fact that.

So in this sentence, it introduces the method or means:

• Azáltal, hogy megmérjük a profilmélységet = By measuring the tread/profile depth

It is a bit more formal than plain English by + -ing.

In this pattern, hogy introduces a full clause.

Hungarian often says:

• azáltal, hogy + clause

Literally, this is something like:

• by means of the fact that + we do X

Here the clause is:

• megmérjük a profilmélységet = we measure the profile depth

English usually prefers by measuring, but Hungarian often uses a full clause with hogy.

Yes, roughly:

• Azáltal = by that means / thereby
• hogy = that
• megmérjük = we measure / we measure completely
• a profilmélységet = the profile depth
• megtaláljuk = we find
• a hibát = the error / fault

A more literal English version would be:

• By the fact that we measure the profile depth, we find the fault.

That sounds unnatural in English, which is why a smoother translation would use by measuring instead.

The prefix meg- often gives the verb a sense of completion, result, or successful accomplishment.

So:

• mérjük = we are measuring / we measure
• megmérjük = we measure it fully, take the measurement

And:

• találjuk by itself is not normally used this way for find
• megtaláljuk = we find it, we succeed in locating it

In this sentence, meg- helps show that these are completed, goal-oriented actions:

1. we measure the depth
2. we find the fault

Because the verb is:

• 1st person plural = we
• in the definite conjugation

So megmérjük means:

• we measure it / we measure the ...

Hungarian uses the definite conjugation when the verb has a definite object, and here the object is:

• a profilmélységet = the profile depth

That is why it is megmérjük, not a form from the indefinite conjugation.

For the same reason: the object is definite.

Here the object is:

• a hibát = the fault / the error

Because the object is specific and marked with the definite article a, Hungarian uses the definite verb form:

• megtaláljuk = we find it / we find the ...

This is a very important feature of Hungarian grammar.

Because they are direct objects, and Hungarian marks direct objects with the accusative ending -t.

So:

• profilmélység = profile depth
• profilmélységet = profile depth as the object

and

• hiba = error, fault
• hibát = error/fault as the object

The extra vowel before -t depends on Hungarian sound patterns:

• profilmélység + -et
• hiba + -t → hibát

So the -t is the key object marker.

Hungarian normally uses the definite article a / az before definite nouns, just as English uses the.

So:

• a profilmélységet = the profile depth
• a hibát = the fault

Each noun phrase gets its own article. Hungarian does not usually "share" one article across two different noun phrases in a sentence like this.

It is a compound noun:

• profil = profile, tread, surface pattern
• mélység = depth

So profilmélység literally means profile depth.

In technical or automotive contexts, this often refers to tread depth.

Hungarian makes compounds very freely, so long nouns like this are common.

Because Hungarian word order is flexible and often reflects focus, topic, or what the speaker wants to foreground.

Starting with:

• Azáltal, hogy megmérjük a profilmélységet...

puts emphasis on the method:

• By measuring the profile depth...

Then the result comes:

• ...megtaláljuk a hibát.
• ...we find the fault.

This is very natural in Hungarian when introducing how something is achieved.

Yes. A common alternative would be something like:

• A profilmélység megmérésével megtaláljuk a hibát.

This also means:

• By measuring the profile depth, we find the fault.

Here, instead of azáltal, hogy + clause, Hungarian uses a noun-like form:

• megmérésével = by its measurement / by measuring it

Both are grammatical, but:

• azáltal, hogy ... feels a bit more clause-based and explicit
• megmérésével is more compact

Yes, in many contexts Hungarian can also use:

• azzal, hogy ...

For example:

• Azzal, hogy megmérjük a profilmélységet, megtaláljuk a hibát.

This is very similar in meaning:

• By measuring the profile depth, we find the fault.

Very broadly:

• azáltal, hogy can sound slightly more formal or written
• azzal, hogy is also common and natural

Because that whole opening part is a subordinate clause-like unit introducing the means or method, and it is separated from the main clause with a comma.

Structure:

• Azáltal, hogy megmérjük a profilmélységet, = subordinate introductory part
• megtaláljuk a hibát. = main clause

This punctuation is normal in Hungarian.

Yes. Both verbs are explicitly first person plural:

• megmérjük = we measure
• megtaláljuk = we find

Depending on context, this could mean:

• an actual group of people
• technicians or inspectors in general
• a more impersonal we like English technical writing sometimes uses

So the grammar really is we, even if the meaning may be somewhat general.