Visszahoztuk a vízhatlan zsákot anélkül, hogy nedves lett volna.

Yes, both are possible, but they are used a bit differently.

• visszahoztuk is the verb hozni (to bring) with the verbal prefix vissza- (back), so literally we-brought-back-it.
• In Hungarian, prefixes are often attached directly to the verb in a neutral statement:
  • Visszahoztuk a zsákot. = We brought back the bag.
• The prefix can separate and move after the verb in certain contexts, especially with focus, negation, or some other sentence patterns:
  • Nem hoztuk vissza a zsákot. = We didn’t bring back the bag.

So here visszahoztuk is the normal neutral form.

Because Hungarian is using the definite conjugation.

The object is a vízhatlan zsákot = the waterproof bag, which is a definite object. When the direct object is definite, Hungarian often uses a special set of verb endings.

• hoztunk = we brought (indefinite conjugation)
• hoztuk = we brought it / we brought the ... (definite conjugation)

So:

• Hoztunk egy zsákot. = We brought a bag.
• Hoztuk a zsákot. = We brought the bag.

That is why the sentence has visszahoztuk, not visszahoztunk.

Because it is the direct object of the verb, so it takes the accusative ending.

• basic form: zsák = bag
• accusative form: zsákot = bag as a direct object

The accusative ending is usually -t, but in many words an extra linking vowel appears, which is why you get -ot here.

So:

• a zsák = the bag
• a zsákot = the bag as the thing being brought back

vízhatlan means waterproof or impermeable to water.

It is made up of:

• víz = water
• -hatatlan = a form meaning something like cannot be ...-ed or not susceptible to ...

So the word suggests something like not penetrable by water.

A learner may also see vízálló, which also often means water-resistant / waterproof in everyday Hungarian. Depending on context:

• vízhatlan often sounds more like watertight / fully waterproof
• vízálló can be more like water-resistant

But in many ordinary situations, people may use them quite similarly.

anélkül, hogy means without followed by a clause.

Literally:

• anélkül = without that / without it
• hogy = that

But in natural English, you usually translate the whole phrase simply as without.

Examples:

• Elment anélkül, hogy szólt volna. = He left without saying anything.
• Befejeztük anélkül, hogy hibáztunk volna. = We finished without making a mistake.

In Hungarian, after anélkül, hogy, you normally use a full clause with a finite verb, rather than just an -ing form like in English.

So English says:

• without getting wet

But Hungarian says something more like:

• without it having become wet

Because anélkül, hogy introduces a subordinate clause, and Hungarian normally separates such clauses with a comma.

So:

• Visszahoztuk a vízhatlan zsákot, anélkül, hogy nedves lett volna.

That comma is standard Hungarian punctuation.

Because anélkül, hogy usually takes a verb form that expresses something non-realized or hypothetical in this kind of sentence.

Here lett volna is the past conditional of lesz / lenni.

• lett = became
• lett volna = would have become / would have been

In this construction, Hungarian often uses this form where English uses without + -ing.

So:

• anélkül, hogy nedves lett volna
  literally: without it having become wet
  natural English: without getting wet

Using nedves volt would sound wrong here, because the structure after anélkül, hogy normally does not work that way.

Because Hungarian uses lett volna as the natural past conditional form of lenni in this type of construction.

Also, there is an important meaning difference:

• nedves volt = it was wet
  this describes a state
• nedves lett = it became/got wet
  this describes a change of state

In this sentence, the intended idea is the bag did not get wet during the process. So lett volna is the right choice.

In natural English we often say without being wet or without getting wet, but Hungarian commonly expresses this as without having become wet.

The subject is understood from context: it refers to a vízhatlan zsák.

Hungarian often leaves out pronouns when they are clear from the situation.

So the clause means:

• anélkül, hogy nedves lett volna
• literally: without [it] having become wet

The it does not need to be stated, because Hungarian can leave it implicit.

Because nedves is an adjective meaning wet, and here it is part of the predicate, not a noun phrase.

Compare:

• A zsák nedves. = The bag is wet.
• A zsák egy nedves dolog. = The bag is a wet thing.

In the sentence you gave, nedves lett volna means would have become wet, so nedves is acting as a predicate adjective. No article is needed.

The word order is quite normal.

• Visszahoztuk = the verb
• a vízhatlan zsákot = the object
• anélkül, hogy nedves lett volna = the without clause

So the sentence is structured roughly like:

• We brought back the waterproof bag, without it having gotten wet.

Hungarian word order is flexible, but this version is neutral and natural.

You could move things around for emphasis, but the given order is straightforward.

Yes. In natural English, without getting wet is usually the best translation.

Even though Hungarian uses nedves lett volna, which is closer to without having become wet, the most idiomatic English rendering is:

• We brought back the waterproof bag without it getting wet.

Depending on context, without being wet may also work, but without getting wet better reflects the idea of avoiding a change of state.

Yes, nedves is a normal word for wet or damp.

However, Hungarian also has related words with slightly different shades of meaning:

• nedves = wet / damp
• vizes = watery / wet / covered with water

In some contexts, vizes might also be possible, but nedves lett volna is perfectly natural and idiomatic here.

It can be used with many verbs. The pattern is very common.

Examples:

• Elment anélkül, hogy elköszönt volna.
  He left without saying goodbye.

• Bejött anélkül, hogy kopogott volna.
  He came in without knocking.

• Megoldották anélkül, hogy segítséget kértek volna.
  They solved it without asking for help.

So the important pattern to learn is:

• anélkül, hogy + verb (often in past conditional form)

This is one of the standard Hungarian ways to say without doing something.