Hvis mine sokker mangler igen, ligger de måske stadig i kurven ved vaskemaskinen.

Hvis means if here, and it introduces a subordinate clause.

So the sentence is made of:

• Hvis mine sokker mangler igen = the condition
• ligger de måske stadig i kurven ved vaskemaskinen = the main clause

A very natural way to think about it is:

• If my socks are missing again...
• ...they may still be in the basket by the washing machine.

This is one of the most important word-order patterns in Danish.

In a main clause, Danish normally follows the V2 rule: the finite verb comes in the second position.

Here, the whole Hvis-clause comes first:

• Hvis mine sokker mangler igen

Because that takes up the first position, the verb of the main clause must come next:

• ligger

Then the subject comes after it:

• de

So:

• Hvis mine sokker mangler igen, ligger de måske stadig...

If the main clause stood alone, it would be:

• De ligger måske stadig i kurven ved vaskemaskinen.

Yes, mangle can mean to lack, but it is also commonly used to mean to be missing / not be there.

That means Danish can use it in two related ways:

• Jeg mangler mine sokker = I’m missing my socks / I don’t have my socks
• Mine sokker mangler = My socks are missing

So in your sentence, mine sokker mangler igen means that the socks are absent again.

This is different from savne, which means to miss in an emotional sense:

• Jeg savner dig = I miss you

You would not use savner for lost socks.

Danish often prefers position verbs where English would simply use to be.

Common ones include:

• ligge = lie
• stå = stand
• sidde = sit

For things like clothes, papers, socks, and other loose objects resting somewhere, ligge is very natural.

So:

• De ligger i kurven = They’re lying / they are in the basket

You could sometimes hear er in broader contexts, but ligger sounds more specific and natural here because socks are understood as physically lying in the basket.

Because sokker is plural, the possessive must also take the plural form:

• min = for singular common gender
• mit = for singular neuter
• mine = for plural

So:

• min sok = my sock
• mine sokker = my socks

This is the same pattern as:

• min bog = my book
• mit hus = my house
• mine bøger = my books

Because sokker is plural.

In Danish, the third-person pronouns are:

• den = singular common gender
• det = singular neuter
• de = plural

Since mine sokker is plural, the correct pronoun is de:

• Mine sokker ... de ...

If it were singular, you would use den or det depending on the noun’s gender.

They each add a different nuance:

• igen = again
• måske = maybe / perhaps
• stadig = still

So the sentence suggests:

• the socks are missing again
• they are maybe
• still in the basket

Each adverb modifies a different part of the situation:

• mangler igen = are missing again
• måske stadig = maybe still

This is the most neutral Danish order here.

After the main-clause verb and subject, adverbs often come in a fairly natural sequence:

• ligger = verb
• de = subject
• måske = sentence adverb
• stadig = time/state adverb

So:

• ligger de måske stadig i kurven

A useful comparison:

• De ligger måske stadig i kurven.
• Hvis ..., ligger de måske stadig i kurven.

Once the Hvis-clause is moved to the front, the verb comes before the subject, but the rest of the adverb pattern stays natural.

Because the two prepositions describe different kinds of location.

• i kurven = in the basket
  This means the socks are inside it.

• ved vaskemaskinen = by / near the washing machine
  This means the basket is located next to the washing machine.

So:

• i is used for being inside something
• ved is used for being at, by, or near something

That -en is the definite ending in Danish.

Instead of usually putting a separate word like the before the noun, Danish often attaches definiteness to the noun itself.

Examples:

• en kurv = a basket

• kurven = the basket

• en vaskemaskine = a washing machine
• vaskemaskinen = the washing machine

So:

• i kurven = in the basket
• ved vaskemaskinen = by the washing machine

Yes. Danish commonly forms compound nouns as a single word.

So:

• vaske = wash
• maskine = machine
• vaskemaskine = washing machine

Then the definite form becomes:

• vaskemaskinen = the washing machine

This is very normal in Danish. English often writes these as two words, but Danish usually joins them.

Yes. The comma marks the end of the opening subordinate clause:

• Hvis mine sokker mangler igen,
• ligger de måske stadig i kurven ved vaskemaskinen.

In a sentence like this, the comma helps show where the condition ends and the main statement begins.

It is especially useful because the word order changes in the main clause right after the comma.

Yes, that is possible.

Adding så after an if-clause is common in Danish, especially in speech:

• Hvis mine sokker mangler igen, så ligger de måske stadig i kurven ved vaskemaskinen.

The version without så is also completely natural and a bit leaner in style.

So both are fine:

• Hvis ..., ligger de ...
• Hvis ..., så ligger de ...

The original sentence is perfectly normal as it stands.