Hvis den her ledning ligger på gulvet, falder børnene måske over den.

Den her ledning is the very common everyday way to say this cable/wire in Danish.

A few useful comparisons:

• den her ledning = this cable/wire
• denne ledning = this cable/wire, but more formal or written
• ledningen = the cable/wire

A key grammar point is that after den her / det her / de her, the noun usually stays in the indefinite form:

• den her bog
• det her hus
• de her børn

So den her ledning is correct, not den her ledningen.

Here, her helps turn den into this.

So:

• den her = this
• den der = that

Literally, her means here, but in this kind of phrase it works like a demonstrative marker.

So den her ledning is basically this cable here, but in normal English we just say this cable.

Danish often prefers a position verb where English would often just use is.

Here, ligger means lies / is lying and is natural for something like a cable on the floor.

So:

• Ledningen ligger på gulvet = The cable is lying on the floor

You can say er på gulvet, but ligger på gulvet sounds more specific and more natural because it describes the physical position of the cable.

This is very common in Danish:

• bogen ligger på bordet = the book is on the table
• stolen står i hjørnet = the chair is in the corner
• han sidder i sofaen = he is sitting on the sofa

Because gulvet is the definite form of gulv.

• et gulv = a floor
• gulvet = the floor

The noun gulv is a neuter noun, so its definite singular ending is -et.

That is why Danish says:

• på gulvet = on the floor

This is because of Danish V2 word order in main clauses.

The sentence starts with a subordinate clause:

• Hvis den her ledning ligger på gulvet, ...

After that, the main clause begins. In Danish main clauses, the finite verb normally comes in the second position. Since the hvis-clause takes the first position, the verb comes next:

• Hvis ..., falder børnene måske over den.

So the structure is:

1. Hvis den her ledning ligger på gulvet
2. falder
3. børnene
4. måske
5. over den

If the main clause came first, you would say:

• Børnene falder måske over den, hvis den her ledning ligger på gulvet.

In a normal Danish main clause, words like måske, ikke, jo, and nok often come in the sentence adverb position, which is usually after the finite verb and the subject.

So here:

• falder = finite verb
• børnene = subject
• måske = sentence adverb

That gives:

• falder børnene måske over den

Compare:

• Børnene falder måske over den
• Falder børnene måske over den?

So the position of måske is normal Danish word order.

Danish often uses the present tense where English uses a future idea.

So in Danish, a sentence like this can describe a possible future consequence without any special future tense:

• Hvis den her ledning ligger på gulvet, falder børnene måske over den.

The sense of possibility comes from:

• hvis = if
• måske = maybe / perhaps / might

So Danish does not need a separate future form here. The present tense is completely normal.

Here, falde over noget means to trip over something or to fall over something because it is in your way.

So:

• falde over den = trip over it

The den refers back to ledning.

Be aware that falde over can sometimes mean something else in other contexts, such as come across / stumble upon, but in this sentence the physical meaning is clearly intended.

Børnene means the children, while børn just means children.

In this sentence, Danish uses the definite form because it is talking about the children relevant to the situation: the children who might be in that place.

So:

• børn = children
• børnene = the children

If you said børn, it would sound more general, less tied to a specific situation.

Because ledning is a common-gender noun:

• en ledning

When you refer back to a common-gender noun with a pronoun, you use den:

• ledning → den

If it were a neuter noun, you would use det instead:

• et bord → det

Also, after the preposition over, Danish uses the pronoun in the normal object form:

• over den = over it

So over den is exactly what you would expect here.