Zet elke verhuisdoos in de aanhanger.

Because this is an imperative sentence: a command or instruction.

• zetten = to put / place / set
• zet = the imperative form used when telling someone to do it

In Dutch, commands often begin directly with the verb:

• Zet de doos neer. = Put the box down.
• Kom hier. = Come here.
• Wacht even. = Wait a moment.

The subject jij/je is usually omitted in commands, just like English often omits you.

Zetten is the infinitive: to put / to place.

Zet is a conjugated form. In this sentence, it is specifically the imperative singular:

• zetten = to put
• ik zet = I put
• jij zet = you put
• zet! = put!

So the dictionary form is zetten, but the sentence uses zet because it is giving an instruction.

Dutch often distinguishes between different kinds of placing verbs more than English does.

• zetten is often used for putting something standing, upright, or in a general placed position
• leggen is often used for putting something lying down
• doen can sometimes mean put in casual speech, depending on context

With a box, especially in practical instructions, zetten is very normal. Even if the box is not literally “standing upright” in a strict sense, Dutch often uses zetten for placing objects like boxes, bags, furniture, and containers.

So Zet elke verhuisdoos in de aanhanger sounds natural.

Both are possible, but they mean things a little differently.

• elke verhuisdoos = each/every moving box
• alle verhuisdozen = all the moving boxes

With elke, Dutch uses a singular noun:

• elke doos
• elke verhuisdoos

With alle, Dutch usually uses a plural noun:

• alle dozen
• alle verhuisdozen

So:

• Zet elke verhuisdoos in de aanhanger. = Put each moving box in the trailer.
• Zet alle verhuisdozen in de aanhanger. = Put all the moving boxes in the trailer.

In many situations, the practical meaning is very close.

Because Dutch very often forms compound nouns by writing them as a single word.

• verhuizen = to move house
• doos = box
• verhuisdoos = moving box / packing box

This is extremely common in Dutch:

• treinstation = train station
• huisdeur = house door / front door
• appelboom = apple tree

English often writes these as two words, but Dutch usually joins them into one.

A verhuisdoos is a box used when moving house—basically a moving box, packing box, or cardboard box for moving.

It comes from:

• verhuizen = to move house
• doos = box

So it is not just any random box; it suggests a box used during a move.

Because aanhanger is a de-word in Dutch.

Dutch nouns take either:

• de
• het

There is no completely reliable shortcut for all nouns, so this usually has to be learned with the noun:

• de aanhanger = the trailer

A useful habit is to learn nouns with their article from the beginning:

• de doos
• de verhuisdoos
• de aanhanger

That will help a lot later with adjective endings and pronouns.

Here, aanhanger means trailer: something attached to a car or other vehicle for carrying things.

Be careful: aanhanger can also mean supporter or follower in other contexts.

For example:

• een aanhanger van die partij = a supporter of that party
• de aanhanger achter de auto = the trailer behind the car

In your sentence, because we are talking about moving boxes, aanhanger clearly means trailer.

Because in focuses on putting something inside the trailer.

• in de aanhanger = in the trailer / into the trailer
• naar de aanhanger = toward the trailer / to the trailer

If you are placing the boxes inside it, in is the natural choice.

Dutch often uses in with a verb of placement:

• Zet het in de kast. = Put it in the cupboard.
• Leg het in de doos. = Put it in the box.

English sometimes distinguishes in and into more clearly, but Dutch often just uses in here.

Because in a Dutch main clause imperative, the verb usually comes first.

The basic structure here is:

• Zet = verb
• elke verhuisdoos = direct object
• in de aanhanger = prepositional phrase showing location/destination

So the order is very normal:

Verb + object + place

You could sometimes move parts around for emphasis, but this version is the most neutral and natural.

Yes, normally elke takes a singular countable noun.

Examples:

• elke dag = every day
• elke stoel = every chair
• elke verhuisdoos = every moving box

So elke verhuisdozen would be incorrect.

If you want a plural idea, you would use something like:

• alle verhuisdozen = all moving boxes

In informal spoken Dutch, some speakers do use doen in a general put sense, but zet is better and more precise here.

• Zet ... in de aanhanger sounds natural and standard.
• Doe ... in de aanhanger may sound more casual or less careful, depending on region and context.

For a learner, zet is the safer and more idiomatic choice in this sentence.

Dutch can use the same imperative form for more than one person in many everyday situations:

• Zet elke verhuisdoos in de aanhanger.

If you want to make the plural or polite form explicit, Dutch can add u or jullie, but the bare imperative is very common.

Examples:

• Zet elke verhuisdoos in de aanhanger. = Put each moving box in the trailer.
• Zet u elke verhuisdoos in de aanhanger. = Put each moving box in the trailer. (formal, less common in this kind of instruction)
• Zetten jullie elke verhuisdoos in de aanhanger. is not the normal imperative pattern.

So in practice, the original sentence works well as a general instruction.

You would usually say:

Zet alle verhuisdozen in de aanhanger.

Changes:

• elke → alle
• verhuisdoos → verhuisdozen (plural)

So:

• elke verhuisdoos = each moving box
• alle verhuisdozen = all the moving boxes

That is probably the most common alternative version of the sentence.