Meet de kast op en monteer hem.

Because this sentence is giving commands.

• meten = to measure
• monteren = to assemble / install
• meet = measure!
• monteer = assemble!

So Meet de kast op en monteer hem uses the imperative form, just like English Measure the cabinet and assemble it.

No. Here meet is the command form of the Dutch verb meten, which means to measure.

So even though meet looks exactly like the English word meet, it has a completely different meaning in this sentence. It is basically a false friend for English speakers.

Because the full verb is opmeten, and opmeten is a separable verb.

In Dutch, many verbs have a main part plus a particle such as op, aan, uit, mee, and so on. In a main clause or a command, that particle often moves to the end.

So:

• dictionary form: opmeten
• command: Meet de kast op
• main clause: Ik meet de kast op

That is why you do not see opmeet here.

A very useful rule is:

• split in main clauses and commands
• together in infinitives and many verb-final forms

Examples:

• Ik meet de kast op.
• Meet de kast op.
• Ik wil de kast opmeten.
• Omdat ik de kast opmeet...
• Ik heb de kast opgemeten.

So in your sentence, Meet de kast op, the split form is correct because it is a command.

Meten means to measure in a general sense.

Opmeten often means to measure something up, to take the dimensions of something, or to measure it properly for practical use.

So:

• meten = measure
• opmeten = measure up / take the measurements of

With furniture, rooms, walls, windows, and similar objects, opmeten is often the more natural choice when you mean taking the dimensions carefully.

Because kast is a de-word in Dutch.

Dutch singular nouns take either de or het, and this is something you usually have to learn with each noun.

So:

• de kast = correct
• het kast = incorrect

A useful extra detail:

• singular: de kast
• plural: de kasten
• diminutive: het kastje

That last one changes to het because Dutch diminutives are always het-words.

Because hem is a normal object pronoun for a singular de-word like de kast.

So the sentence refers back to de kast with hem:

• de kast → hem

Why not het? Because het is normally used for het-words, not for de kast.

Why not haar? That can also occur with some de-words, especially depending on region, style, or whether speakers feel the noun is feminine. But in everyday Dutch, especially in the Netherlands, hem is very common for non-person singular de-words.

So for a learner, de kast ... hem is a good and natural pattern to know.

Because commands usually leave out the subject in Dutch, just like in English.

Compare:

• English: Measure the cabinet
• Dutch: Meet de kast op

The implied subject is you, but it does not need to be said.

You can add jij or je for emphasis, contrast, or irritation, but that is not the neutral default. The plain imperative normally has no stated subject.

Because with separable verbs, the object usually sits between the verb stem and the separated particle.

So the pattern is:

• verb stem + object + particle

In this sentence:

• Meet = verb stem
• de kast = object
• op = separated particle

That gives:

• Meet de kast op

This word order is completely normal in Dutch for separable verbs.