Hun vasker både lagenet og pudebetrækket, fordi alt skal være rent til i morgen.

Vasker is the present tense form of the verb at vaske.

• at vaske = to wash
• vasker = washes / is washing

So Hun vasker ... means She washes ... or She is washing ..., depending on context.

In Danish, the present tense is often used in places where English might use either simple present or present continuous.

Både ... og means both ... and.

So:

• både lagenet og pudebetrækket = both the sheet and the pillowcase

It is a very common structure in Danish:

• Han taler både dansk og engelsk = He speaks both Danish and English
• Jeg kan lide både kaffe og te = I like both coffee and tea

Because they are in the definite form, meaning the sheet and the pillowcase.

In Danish, many nouns add the definite article as an ending instead of using a separate word like the.

• et lagen = a sheet

• lagenet = the sheet

• et pudebetræk = a pillowcase
• pudebetrækket = the pillowcase

This is very different from English, where the stands before the noun.

It is a compound noun, which is very common in Danish.

• pude = pillow
• betræk = cover

So:

• pudebetræk = pillow cover, meaning pillowcase
• pudebetrækket = the pillowcase

Danish often combines smaller words into one longer noun, just like German does.

Fordi means because.

It introduces the reason:

• Hun vasker både lagenet og pudebetrækket = She is washing both the sheet and the pillowcase
• fordi alt skal være rent til i morgen = because everything must be clean by tomorrow

So the second part explains why she is washing them.

Yes. Fordi introduces a subordinate clause, and subordinate clauses in Danish usually have different word order from main clauses.

Here we get:

• fordi alt skal være rent

This is the normal subordinate-clause order:

• conjunction: fordi
• subject: alt
• finite verb: skal
• infinitive / complement: være rent

A very useful thing to remember is that in subordinate clauses, sentence adverbs such as ikke usually come before the finite verb:

• fordi alt ikke skal være beskidt

That differs from main clause order.

Skal være means must be or has to be.

• alt er rent = everything is clean
• alt skal være rent = everything must be clean

So skal adds the idea of necessity, requirement, or expectation.

In this sentence, the meaning is that everything needs to be clean by tomorrow, not necessarily that it is already clean now.

This is adjective agreement.

The adjective is ren = clean, but it changes form depending on what it describes:

• ren = common gender singular
• rent = neuter singular
• rene = plural or definite

Here the word being described is alt = everything. Grammatically, alt behaves like a neuter singular word, so the adjective becomes rent.

That is why we say:

• alt skal være rent

not ren and not rene.

Alt means everything.

It can also literally be understood as all of it, depending on context. In this sentence it refers to all the bedding or all the relevant things that need to be clean.

Examples:

• Alt er godt = Everything is good
• Jeg har spist alt = I have eaten everything

As mentioned, alt takes singular neuter agreement, which is why we get rent.

Til i morgen means for tomorrow or by tomorrow, depending on context.

In this sentence, the most natural meaning is by tomorrow:

• alt skal være rent til i morgen = everything must be clean by tomorrow

It suggests a deadline or a state that needs to be true when tomorrow comes.

Also note that i morgen is normally written as two words in standard Danish.

Yes. You could say:

• Hun vasker lagenet og pudebetrækket ...

That still means she is washing the sheet and the pillowcase.

Adding både makes the pairing more explicit and gives the sense of both, which can sound a little more natural when you want to emphasize that she is washing both items, not just one of them.