Keresem a szerszámokat, de nem tudom, a csavarok is a dobozban vannak-e.

Because keres is being used with a definite direct object: a szerszámokat = the tools.

Hungarian verbs often have two sets of endings:

• indefinite conjugation: used when there is no definite object
• definite conjugation: used when the object is definite

So:

• keresek = I am looking / I look (for something unspecified)
• keresem a szerszámokat = I am looking for the tools

The -em ending shows I plus definite object.

That ending contains two things:

• -ok = plural
• -at = accusative marker (direct object)

Step by step:

• szerszám = tool
• szerszámok = tools
• szerszámokat = tools (as the object of the verb)

Since I am looking for the tools, tools is the direct object, so Hungarian marks it.

In this sentence it naturally means I am looking for the tools.

Hungarian present tense often covers both:

• I look for
• I am looking for

The exact English translation depends on context. Here, because it describes an ongoing situation, English normally uses am looking for.

Because a/az means the, and the sentence is talking about a specific set of tools, not just tools in general.

• szerszámokat = tools
• a szerszámokat = the tools

That definiteness is also why the verb is keresem rather than keresek.

Literally, nem tudom is I do not know it.

In natural English, we usually just say I don't know.

The form tudom is the definite form of tud, because Hungarian treats the following clause as the thing that is known or not known:

• nem tudom = I don't know
• more literally: I don't know it/that

So the whole clause a csavarok is a dobozban vannak-e functions as what is not known.

The -e marks a yes/no question, especially inside an embedded clause.

Here it means something like whether or if in English:

• nem tudom, ... vannak-e = I don't know whether ... are

So:

• a csavarok is a dobozban vannak-e
  = whether the screws are also in the box

This -e is very common in indirect yes/no questions.

Because in standard spelling, this question particle is written attached to the verb with a hyphen.

So:

• van-e = is there? / whether there is
• vannak-e = are there? / whether they are

It is not a separate word here.

Because a csavarok is the subject of the embedded clause, not the object.

In:

• a csavarok is a dobozban vannak-e

the screws are the things that are in the box, so they are the subject of vannak.

The thing that is the object of nem tudom is not csavarok by itself, but the whole clause:

• [a csavarok is a dobozban vannak-e]

So csavarok stays in its basic form: screws.

Here is means also or too.

• a csavarok is = the screws too / the screws also

So the speaker is not only asking about the tools, but also about the screws.

A useful point: Hungarian is usually comes after the word or phrase it belongs to.

• a csavarok is = the screws too
• én is = me too / I too

It is not related to the English verb is.

It means in the box.

Breakdown:

• doboz = box
• -ban / -ben = in
• a dobozban = in the box

The choice between -ban and -ben depends on vowel harmony. Since doboz takes back-vowel endings, it becomes dobozban.

Because csavarok is plural: screws.

Hungarian uses:

• van = is
• vannak = are

So:

• A csavar a dobozban van. = The screw is in the box.
• A csavarok a dobozban vannak. = The screws are in the box.

This is a normal, neutral order for an embedded clause meaning whether the screws are also in the box.

Very roughly:

• a csavarok is = the screws too
• a dobozban = in the box
• vannak-e = are / whether they are

Hungarian word order is flexible, but it often reflects emphasis. This version sounds neutral. If you moved things around, the meaning would stay similar, but the emphasis could change.

Yes, Hungarian can also say:

• Nem tudom, hogy a csavarok is a dobozban vannak-e.

That hogy is often optional in this kind of sentence. Without it, the sentence is still completely natural.

So both are possible:

• Nem tudom, a csavarok is a dobozban vannak-e.
• Nem tudom, hogy a csavarok is a dobozban vannak-e.

Both mean the same thing.