Die Naht braucht eine breite Nahtzugabe.

Because the subject is die Naht, which is third-person singular.
So the verb brauchen is conjugated as braucht:

• ich brauche
• du brauchst
• er/sie/es braucht

If the subject were plural, you would use brauchen:

• Die Nähte brauchen ...

In a normal German main clause, the conjugated verb usually comes second. This is often called the V2 rule.

So in:

• Die Naht = first element
• braucht = second element

That is standard German word order for a statement.

This is about definite vs. indefinite articles, just like the and a/an in English.

• die Naht = the seam
• eine breite Nahtzugabe = a wide seam allowance

So the sentence is talking about a particular seam, but it says that it needs a seam allowance of a certain kind.

Also, both nouns are feminine singular, which is why you see die and eine.

That is a very good question, because die can mean:

• feminine singular
• or plural

Here, the verb tells you the answer:

• braucht = singular
• brauchen = plural

So die Naht braucht ... must be singular.

If it were plural, you would get:

• Die Nähte brauchen ...

It is in the accusative case, because it is the direct object of braucht.

The seam is doing the needing:

• Die Naht = subject

The thing needed is:

• eine breite Nahtzugabe = direct object

So the structure is:

• subject + verb + accusative object

Because adjective endings in German depend on:

• gender
• case
• article

Here you have:

• eine = feminine singular
• Nahtzugabe = feminine singular
• accusative

After eine in the feminine singular accusative, the adjective takes -e:

• eine breite Nahtzugabe

This is the normal pattern.

Yes, Nahtzugabe is one compound noun.

German often combines nouns into a single word. Here:

• Naht
  • Zugabe = Nahtzugabe

The last part usually determines the basic meaning and the grammatical gender.
Since die Zugabe is feminine, die Nahtzugabe is also feminine.

This kind of word-building is extremely common in German.

In German compound nouns, the last part decides the gender.

So:

• die Zugabe = feminine
• therefore die Nahtzugabe = feminine

Even though Naht is also feminine here, the important rule is that the final element controls the gender.

Because all nouns are capitalized in German.

So in this sentence:

• Naht is a noun
• Nahtzugabe is a noun

That is why they begin with capital letters.

Sometimes yes, but the normal, neutral version is:

• Die Naht braucht eine breite Nahtzugabe.

You could move another element to the front for emphasis, but here that may sound marked or even unclear, because:

• die Naht and eine breite Nahtzugabe are both singular noun phrases
• the case marking is not very obvious on the surface

So for a learner, the original word order is the safest and most natural choice.

A simple pronunciation guide is:

• Die = dee
• Naht = roughly naht with a long a
• braucht = roughly browkht
• eine = EYE-nuh
• breite = BRYE-tuh
• Nahtzugabe = roughly NAHT-tsoo-gah-buh

A few useful notes:

• Naht has a long vowel: naaht
• ei in eine and breite sounds like English eye
• ch in braucht is not an English sound; it is a throat/friction sound

Yes, you can say:

• Die Naht benötigt eine breite Nahtzugabe.

But braucht is usually more everyday and natural.
benötigt sounds a bit more formal or technical.

So for most situations, braucht is the more common choice.