Hvis hækken havde været lavere, ville vi have set, at hækkesaksen lå ved døren hele tiden.

It is a past unreal (counterfactual) conditional.

The pattern is:

• Hvis + havde + past participle = the unreal condition
• ville + have + past participle = the unreal result

So:

• Hvis hækken havde været lavere = if the hedge had been lower
• ville vi have set = we would have seen

This tells you the speaker is talking about something that did not actually happen in the past.

Havde været is the past perfect of være.

Danish uses this in the if-clause of a past unreal conditional, just like English uses had been:

• Hvis hækken havde været lavere = If the hedge had been lower

It shows that the condition belongs to an earlier, unreal past situation.

Yes, but it would mean something different.

• Hvis hækken havde været lavere = past unreal: the hedge was not lower, and because of that, something was not seen
• Hvis hækken var lavere = present or more general unreal/hypothetical situation: if the hedge were lower

So the original sentence is specifically about a missed situation in the past, not a present hypothetical.

This is because of Danish word order in main clauses.

The whole Hvis... clause comes first, and after that Danish follows the V2 rule: the finite verb comes in second position. So the structure is:

• Hvis hækken havde været lavere,
• ville vi have set ...

Even though vi is the subject, ville must come first in the main clause because the sentence already started with another element.

Because ville have set is the Danish equivalent of would have seen.

You need:

• ville = would
• have
• set = seen

So ville have set is a conditional perfect form. You cannot say ville set here.

Because set is the past participle of se, while så is the simple past.

Compare:

• vi så = we saw
• vi har set = we have seen
• vi ville have set = we would have seen

After have, Danish uses the past participle, so set is required.

Here, hvis is the normal word for if in a condition.

• hvis = if
• om = whether, and sometimes if in other contexts

In a clear conditional sentence like this one, hvis is the standard choice:

• Hvis hækken havde været lavere...

Using om here would sound wrong in standard written Danish.

Because Danish usually puts the definite article at the end of the noun.

• en hæk = a hedge
• hækken = the hedge

So -en here means the. This noun is common gender, which is why the definite ending is -en.

It is singular definite:

• en hækkesaks = a hedge trimmer / a pair of hedge shears
• hækkesaksen = the hedge trimmer / the hedge shears

This can feel strange to English speakers because English often uses a plural-looking word such as scissors or shears. Danish hækkesaks is treated as a singular noun.

Also, hækkesaks is a compound noun, and Danish forms compounds very freely.

Because Danish often uses position verbs where English would simply use be.

Here, ligge means to lie / be lying / be situated for something resting in a position. Its past tense is lå.

So:

• hækkesaksen lå ved døren = the hedge trimmer was lying / was located by the door

If you said var ved døren, it would sound less natural for an object in this context and would focus less on its physical position.

Here at introduces a subordinate clause, much like English that:

• vi ville have set, at hækkesaksen lå ved døren
• we would have seen that the hedge trimmer was by the door

In English, that is often optional. In Danish, at is very common and helps clearly mark the clause.

Because the sentence is reporting what we would have seen at that time.

The clause at hækkesaksen lå ved døren presents the situation as it existed at the relevant past moment: the hedge trimmer was lying there.

Using havde ligget would push that state even further back and change the time relationship. The original version is the natural one for this meaning.

Hele tiden means the whole time, all along, or the entire time.

In this sentence it means that the hedge trimmer had been by the door continuously, and the people simply had not noticed it.

It is very natural for adverbial phrases like this to come late in the clause in Danish:

• ... lå ved døren hele tiden

That end position sounds neutral and idiomatic.

Ved means by, at, or next to.

So:

• ved døren = by the door / near the door

Other prepositions would change the meaning:

• i døren = in the doorway / in the door
• på døren = on the door

So ved is the natural choice if the object was simply located next to the door.

There are two separate points here.

• The comma after lavere is normal because the sentence begins with a subordinate Hvis-clause.
• The comma before at depends on the comma style being used.

In traditional Danish comma style, you write:

• ville vi have set, at ...

In new comma style, that comma before at can be omitted. So the punctuation here is perfectly normal, but you may also see a version without the second comma.