Learn Hardcore Croatian: Djeca trče hodnikom bez da pogledaju stoji li netko na vratima. - The children run through the hallway without looking to see whether someone is standing at the door.

With some verbs of motion (like ići, hodati, trčati), Croatian often uses the instrumental case without a preposition to mean “along / through / by way of” a place:

trčati hodnikom – to run along/through the hallway
hodati parkom – to walk through the park
voziti se cestom – to drive along the road

So in Djeca trče hodnikom, the instrumental hodnikom tells you where / along what path they are running.

Why is there no preposition like u or kroz before hodnikom, when in English we say “in the hallway” or “through the hallway”?

Croatian has two main options here:

Instrumental without a preposition
- Djeca trče hodnikom. – The children are running along/through the hallway.
  This is very natural and common.
Preposition + accusative
- Djeca trče kroz hodnik. – The children are running through the hallway.

The meaning is almost the same. The version with the instrumental (hodnikom) is a bit more compact and idiomatic; kroz hodnik explicitly highlights movement “through” something. Both are correct; you just don’t need u or kroz when you choose the instrumental pattern.

What does bez da mean, and how is it different from just bez?

bez + genitive noun = “without (something)”
- bez šećera – without sugar
- bez djece – without children
bez da + finite clause = “without (doing something) / without (someone) doing something”
- bez da pogledaju – without (them) looking
- bez da mi kažeš – without you telling me

So in your sentence:

bez da pogledaju stoji li netko na vratima
= without looking to see whether someone is standing at the door.

Stylistic note: Some traditional grammars call bez da “colloquial” or “non‑standard” and would prefer a different construction (for example a da ne). But bez da + clause is extremely common and widely accepted in modern spoken and written Croatian.

Is bez da pogledaju the only correct option? Could/should it be something like a da ne pogledaju?

All of these are possible, with slightly different style:

Djeca trče hodnikom bez da pogledaju…
Very common in everyday language; neutral in most modern usage.
Djeca trče hodnikom, a da ne pogledaju…
More in line with traditional “standard” recommendations; sometimes feels a bit more formal or archaic.
Djeca trče hodnikom, ne pogledaju ni…
Rephrasing without bez da, using plain negation.

So bez da pogledaju is natural and widely used; a da ne pogledaju is more “by‑the‑book” but less common in casual speech. For normal conversation and most writing, bez da pogledaju is fine.

Why is it pogledaju and not gledaju? What’s the difference?

The difference is aspect:

gledati – imperfective: to look, watch, be looking (ongoing action)
pogledati – perfective: to have a look, to take a quick look (single, complete act)

In bez da pogledaju, the idea is “without even (once) having a look / checking.”
If you said bez da gledaju, it would sound more like “without (at any time) watching,” which doesn’t fit as well: they just need to check the door once, not continuously watch it.

So pogledaju (perfective) matches the notion of a single, brief checking action that doesn’t happen.

Why is the word order stoji li netko and not li stoji netko or netko li stoji?

In Croatian li is a clitic used to form yes‑no questions. Its basic rules:

li comes right after the verb (or after another clitic attached to the verb).
The typical pattern is: Verb + li + Subject/other parts.

So:

Stoji li netko na vratima? – Is someone standing at the door?
Je li on tamo? – Is he there?
Hoće li doći? – Will he come?

Forms like li stoji netko or netko li stoji are ungrammatical in standard Croatian.

In your sentence this question is embedded:

…bez da pogledaju stoji li netko na vratima.
= without looking (to see) whether someone is standing at the door.

Word order inside that embedded question stays the same: stoji li netko.

What kind of clause is stoji li netko na vratima here?

It is an embedded yes‑no question (also called an indirect question).

As a stand‑alone question:
Stoji li netko na vratima? – Is someone standing at the door?
Embedded in another clause, it functions like the object of pogledaju:
pogledati (to see / check) stoji li netko na vratima
= to check whether someone is standing at the door.

So the structure is roughly:
“without looking (to see) whether someone is standing at the door.”

What form is vratima in na vratima, and why is it plural?

Vratima is the locative plural of vrata.

Key points:

vrata (door) is plural‑only in Croatian (a so‑called pluralia tantum noun).
You don’t normally say *vrato for “a door.”
With the preposition na meaning “on / at (a surface or place)”, you use the locative:
- na stolu – on the table
- na podu – on the floor
- na vratima – at/on the door

So na vratima literally means “on/at the doors,” but in English it’s just “at the door” or “in the doorway.”