Voor het sjouwen demonteren we de kast.

Normally yes: We demonteren de kast is the basic word order.

But in this sentence, Voor het sjouwen is placed first for emphasis or context. In a main clause, Dutch then uses verb-second word order, so the finite verb must come next:

• We demonteren de kast.
• Voor het sjouwen demonteren we de kast.

So we moves after the verb. This is very common in Dutch.

Literally, it means for the carrying / hauling.

In more natural English, depending on context, it can mean something like:

• before carrying it
• for moving it
• to make it easier to carry

The idea is that the cupboard is being disassembled in preparation for moving or carrying it.

Because sjouwen is being used as a noun-like infinitive here.

Dutch often turns a verb into a noun by using the infinitive with het:

• eten = to eat
• het eten = the eating / the food / the meal

Similarly:

• sjouwen = to haul, lug, carry heavy things
• het sjouwen = the hauling / carrying

So voor het sjouwen means for the carrying/hauling.

Because this is not an infinitive used after another verb. It is a nominalized infinitive.

Compare:

• We proberen de kast te demonteren. = We try to disassemble the cupboard.
  Here te demonteren is a verbal infinitive.

But:

• het sjouwen = the carrying
  Here sjouwen behaves like a noun, so there is no te.

Not exactly.

Sjouwen means something like:

• to lug
• to haul
• to carry something heavy with effort

It often suggests hard physical work. It is more informal and more vivid than dragen.

Compare:

• dragen = to carry
• tillen = to lift
• sjouwen = to lug / haul / carry with effort

So sjouwen fits well if the cupboard is heavy or awkward.

Yes, absolutely.

That version is grammatically correct and probably the more neutral word order:

• We demonteren de kast voor het sjouwen.

The original sentence:

• Voor het sjouwen demonteren we de kast.

simply puts more focus on the circumstance or purpose first: as for moving it / before carrying it.

It is somewhere between the two in sense.

Literally, voor usually means for. But in this kind of sentence, English may translate it more naturally as before if that is what is meant in context.

So:

• voor het sjouwen
  can suggest
• for the carrying
• in preparation for carrying it
• before moving it

Dutch often leaves that relation a bit more implicit than English does.

Kast is a broad Dutch word for a piece of furniture used for storage. Depending on context, it can mean:

• cupboard
• cabinet
• wardrobe
• closet

So the exact English translation depends on what kind of kast it is. It does not mean the political cabinet.

Yes, it is a normal and common verb, especially for objects, furniture, machines, or parts.

It means:

• to disassemble
• to take apart

It is somewhat more technical than very everyday verbs like uit elkaar halen.

Compare:

• We demonteren de kast. = We disassemble the cupboard.
• We halen de kast uit elkaar. = We take the cupboard apart.

Both are natural, but demonteren sounds a bit more precise.

Yes. Some alternatives are:

• Voordat we de kast sjouwen, demonteren we hem.
  = Before we carry the cupboard, we disassemble it.

• Om de kast te sjouwen, demonteren we hem.
  = To carry the cupboard, we disassemble it.

• Voor het verplaatsen demonteren we de kast.
  = Before moving it / for moving it, we disassemble the cupboard.

Each version gives a slightly different nuance, but the original is concise and natural.