Den der stige er gammel, men den her virker stærk nok.

They are everyday Danish ways to say that and this.

• den der stige = that ladder
• den her = this one / this

Literally, der means there and her means here, so the phrases have a built-in sense of distance:

• den her = the one here → this
• den der = the one there → that

With singular common-gender nouns like stige, you use den. With a neuter noun, you would use det instead:

• det her hus = this house
• det der hus = that house

Because stige is a common-gender noun in Danish.

Danish singular nouns are usually either:

• common gender → takes en in the indefinite form, and den in phrases like this
• neuter → takes et in the indefinite form, and det in phrases like this

So:

• en stige = a ladder
• den her stige = this ladder

If the noun were neuter, you would use det instead:

• et bord = a table
• det her bord = this table

Because after den her / den der, the noun normally stays in its basic singular form.

So you get:

• den her stige
• den der stige

not:

• den her stigen
• den der stigen

This is different from the normal Danish definite form, where the noun often gets a suffixed article:

• stige = ladder
• stigen = the ladder

So think of den her / den der as already doing the job of identifying the noun.

Because they match a singular common-gender noun: stige.

In Danish, adjectives often change form depending on gender and number.

For a common-gender singular noun, the adjective usually stays in the basic form:

• en gammel stige
• stigen er gammel
• den her virker stærk

Compare:

• et gammelt hus = a old house / an old house
• huset er gammelt = the house is old
• to gamle stiger = two old ladders

So here:

• gammel matches stige
• stærk also matches stige, even though the noun is left out in the second clause

Because the noun is already understood from the first clause.

The first clause mentions stige, so in the second clause Danish can simply say den her, meaning this one.

So:

• den der stige er gammel = that ladder is old
• men den her virker stærk nok = but this one seems strong enough

English often uses one here, but Danish usually does not need an extra word. Den her by itself can mean this one when the context is clear.

Here, virker means something like seems, appears, or comes across as.

So:

• den her virker stærk nok = this one seems strong enough

The verb virke can also mean work/function, depending on context:

• Maskinen virker ikke = The machine doesn’t work

But when it is followed by an adjective like stærk, it often means seem/appear:

• hun virker træt = she seems tired
• det virker mærkeligt = that seems strange

Here, nok means enough.

So:

• stærk nok = strong enough

This is a very common pattern in Danish:

• god nok = good enough
• stor nok = big enough
• hurtig nok = fast enough

Be careful, because nok can also mean probably in other sentences:

• Han kommer nok i morgen = He will probably come tomorrow

In your sentence, because nok comes after the adjective stærk, it clearly means enough.

Because men starts a new main clause, and Danish main clauses normally follow the verb-second rule.

That means the finite verb comes in the second position.

Here the order is:

• den her = first element
• virker = second element

So:

• men den her virker stærk nok

If something else came first, the verb would still stay second:

• men i dag virker den her stærk nok = but today this one seems strong enough

So the sentence has normal Danish main-clause word order.

They are very close in meaning, but not identical in style.

• den her stige = very common in everyday spoken Danish
• denne stige = more formal, often more written or careful in style

So a learner will hear den her and den der very often in real conversation.

In everyday speech:

• den her stige = this ladder
• den der stige = that ladder

In more formal Danish, you may also see:

• denne stige = this ladder

Yes, that meaning is still visible.

• her = here
• der = there

That is why these demonstrative phrases feel spatial:

• den her stige = the ladder here → this ladder
• den der stige = the ladder there → that ladder

So even though they function like this and that, they still carry the original idea of physical or mental distance.