Hvis tørklædet går op, binder jeg det igen.

Because tørklædet is the definite singular form: the scarf.

The noun is et tørklæde, so it is a neuter noun. In Danish, neuter nouns usually take -et in the definite singular:

• et tørklæde = a scarf
• tørklædet = the scarf

So the ending -et tells you that the speaker is referring to a specific scarf.

Here går op means something like comes undone or comes untied.

This is one of those Danish verb + particle combinations that you should learn as a unit. The basic verb gå usually means go or walk, and op often means up, but together they can have several idiomatic meanings. In this sentence, with a scarf, it means that the knot or tie loosens.

So tørklædet går op does not mean the scarf goes up here.

Because Danish main clauses follow the verb-second rule.

If the main clause stood alone, it would be:

Jeg binder det igen.

But in the full sentence, the hvis clause comes first:

Hvis tørklædet går op, ...

That whole clause takes the first position, so in the main clause the finite verb must come next:

... binder jeg det igen.

This is very typical Danish word order:

• Jeg binder det igen.
• Hvis tørklædet går op, binder jeg det igen.

Det refers back to tørklædet.

Since tørklæde is a neuter noun (et tørklæde), the pronoun used for it is det.

So:

• tørklædet = the scarf
• det = it

In English, this is just like saying I tie it again.

If the noun had been a common gender noun (en-word), Danish would often use den instead.

Igen means again.

So binder jeg det igen means I tie it again.

Its position is normal Danish word order here. The object pronoun det comes before igen:

• Jeg binder det igen.

That is the most natural placement in this sentence.

Danish often uses the present tense for things that are:

• generally true
• habitual
• future in meaning

This sentence describes what the speaker does whenever that situation happens, so the present tense is natural:

• går op = comes undone
• binder = tie

English does something similar:

• If the scarf comes undone, I tie it again.

So even though it may refer to a future situation, Danish does not need a special future form here.

Sometimes, but the meaning changes slightly.

• hvis = if
• når = when or whenever

With hvis, the sentence presents it as a condition:

• If the scarf comes undone, I tie it again.

With når, it sounds more like the speaker expects it to happen, or that it happens regularly:

• Når tørklædet går op, binder jeg det igen.
• When/whenever the scarf comes undone, I tie it again.

So hvis is the better match for if.

Yes, you can think of gå op as a verb with a particle, and in some forms the two parts are separated.

In this sentence, the finite verb is går, while op stays later in the clause:

• tørklædet går op

But in the infinitive, you see them together:

• at gå op

So it is helpful to learn gå op as a fixed expression with several possible meanings, including the one here: come undone.

Because the sentence begins with a subordinate clause:

Hvis tørklædet går op, = If the scarf comes undone,

After that clause, Danish puts a comma before the main clause:

binder jeg det igen.

So the comma marks the boundary between:

• the hvis clause
• the main clause

This is normal Danish punctuation in sentences like this.