Vandhanen i køkkenet drypper, og der er også noget galt med afløbet under vasken.

Because Danish very often builds nouns as compounds.

• vand = water
• hane = tap/faucet

So vandhane is literally water tap. Then Danish adds the definite ending to the noun itself:

• en vandhane = a faucet / a tap
• vandhanen = the faucet / the tap

English usually keeps these as separate words more often, but Danish commonly joins them.

In Danish, the definite article is usually attached to the end of the noun.

From this sentence:

• vandhanen = the faucet
• køkkenet = the kitchen
• afløbet = the drain
• vasken = the sink

The basic forms are:

• en vandhane
• et køkken
• et afløb
• en vask

So:

• common gender nouns usually take -en in the definite singular
• neuter nouns usually take -et in the definite singular

That is why Danish does not need a separate word like English the in these cases.

No. The prepositions do not change how the definite form works.

• i = in
• under = under

The nouns are definite simply because the speaker means a specific kitchen and a specific sink:

• i køkkenet = in the kitchen
• under vasken = under the sink

English uses the as a separate word. Danish usually puts definiteness on the noun itself.

drypper is the present tense of dryppe, meaning to drip.

• at dryppe = to drip
• drypper = drips / is dripping

A very useful thing about Danish verbs is that they do not change for person:

• jeg drypper
• du drypper
• den drypper

The subject changes, but the present-tense verb form stays the same.

Here der er works like English there is or there are.

• der er også noget galt... = there is also something wrong...

This der is not really the location word there. It is an existential there, a grammatical placeholder.

Compare:

• Der er en fejl. = There is a mistake.
• Bogen er der. = The book is there.

In the first sentence, der is grammatical. In the second, der really means a place.

It is a very common Danish expression:

• der er noget galt med ... = there is something wrong with ...

So:

• der er også noget galt med afløbet = there is also something wrong with the drain

A few useful related patterns:

• Der er noget galt med bilen. = There is something wrong with the car.
• Er der noget galt? = Is something wrong?
• Hvad er der galt med computeren? = What is wrong with the computer?

It is best to learn noget galt med as a chunk.

gal is the basic adjective form. galt is a form that often appears in expressions like this.

In der er noget galt, Danish uses galt because the phrase is impersonal and fixed in usage. For a learner, the safest approach is to memorize:

• noget er galt
• der er noget galt med ...

Also note that gal can mean things like wrong, mad, or crazy depending on context, but in this sentence it clearly means wrong.

Because Danish adverbs like også often come after the finite verb in a main clause.

So this sounds natural:

• der er også noget galt ...

The structure is:

• der = subject placeholder
• er = finite verb
• også = adverb
• noget galt = complement

This word order is very typical in Danish main clauses.

og means and, and here it joins two full main clauses:

1. Vandhanen i køkkenet drypper
2. der er også noget galt med afløbet under vasken

The comma helps separate the two ideas clearly. In writing, Danish often uses commas to mark clause boundaries, especially when two full clauses are linked.

So the sentence is basically:

• The faucet in the kitchen is dripping,
• and there is also something wrong with the drain under the sink.

Yes, a few common ones for English speakers:

• ø in køkkenet and afløbet has no exact English equivalent. A rough guide: it is somewhat like the vowel in British bird, but with rounded lips.
• y in drypper also has no exact English equivalent. It is a rounded front vowel.
• Final endings like -en and -et are often pronounced weakly in natural speech.
• Danish consonants can sound softer than English learners expect.

So even if you know every word, the spoken sentence may sound much less clear at first than the written version suggests.