Die Garnrolle liegt auf der Nähmaschine.

Because the two nouns are in different cases.

• Die Garnrolle is the subject of the sentence, so it is in the nominative case.
  • die Garnrolle = the spool of thread
• auf der Nähmaschine gives the location, and here auf is used with the dative case because it describes where something is.
  • der Nähmaschine = on the sewing machine

So:

• nominative feminine: die
• dative feminine: der

That is why the article changes.

Because German distinguishes between:

• location (where?) → usually dative
• movement toward a destination (where to?) → usually accusative

Here, the sentence says the spool is lying on the sewing machine. It is already there, so this is a location idea.

• Die Garnrolle liegt auf der Nähmaschine. = The spool is lying on the sewing machine.

If you wanted to express movement onto the machine, you would use the accusative:

• Ich lege die Garnrolle auf die Nähmaschine. = I put the spool onto the sewing machine.

This is a very common pattern with two-way prepositions like auf.

liegt is the verb liegen, which means to lie or to be lying.

German often uses specific position verbs where English might simply use is:

• liegen = to lie / to be lying (typically for things resting horizontally or simply placed somewhere)
• stehen = to stand
• sitzen = to sit

So Die Garnrolle liegt auf der Nähmaschine is more natural than Die Garnrolle ist auf der Nähmaschine.

You can sometimes say ist auf ..., but liegt gives a more precise, idiomatic description of the object’s position.

Yes. Garnrolle is a compound noun:

• Garn = thread / yarn
• Rolle = roll / spool

Together, Garnrolle means spool of thread.

German very often combines nouns into a single word. English usually uses separate words or of:

• Nähmaschine = sewing machine
• Haustür = house door / front door
• Schlafzimmer = bedroom

The last part of the compound is the main noun, and it determines the gender. Since die Rolle is feminine, die Garnrolle is also feminine.

In both cases, the final part of the compound determines the gender.

• die Rolle → therefore die Garnrolle
• die Maschine → therefore die Nähmaschine

So both nouns are feminine.

This is a very helpful rule for German compounds:

• look at the last noun
• its gender becomes the gender of the whole compound

Nähmaschine is another compound noun:

• näh- comes from nähen = to sew
• Maschine = machine

So Nähmaschine literally means sewing machine.

The ä is related to the verb nähen. You will often see this kind of vowel change in related words.

Because in German, all nouns are capitalized.

So in this sentence:

• Garnrolle
• Nähmaschine

both begin with capital letters because they are nouns.

This is one of the most noticeable spelling differences between German and English.

Yes. It is very normal German word order:

• Die Garnrolle = subject
• liegt = verb
• auf der Nähmaschine = prepositional phrase giving location

German main clauses usually put the finite verb in second position:

• Die Garnrolle liegt auf der Nähmaschine.

You could move the location phrase to the front for emphasis:

• Auf der Nähmaschine liegt die Garnrolle.

That is also correct, but then the verb still stays in second position.

A rough pronunciation guide is:

• Nähmaschine ≈ NAY-muh-shee-nuh

A few notes:

• ä in Näh- is pronounced somewhat like the vowel in English say, but without turning it into a strong English diphthong.
• sch is like English sh
• final -e in German is usually a soft uh sound

So:

• Näh → roughly neh / nay
• ma-schi-ne → muh-shee-nuh

Yes, that is understandable and grammatically correct, but liegt is usually better.

Compare:

• Die Garnrolle ist auf der Nähmaschine.
  = The spool is on the sewing machine.
• Die Garnrolle liegt auf der Nähmaschine.
  = The spool is lying on the sewing machine.

The second sounds more natural when talking about the physical position of an object. German often prefers a position verb instead of a simple form of sein.

The likely plurals are:

• die Garnrolle → die Garnrollen
• die Nähmaschine → die Nähmaschinen

So you could say:

• Die Garnrollen liegen auf der Nähmaschine.
  = The spools of thread are lying on the sewing machine.

Notice that the verb changes too:

• singular: liegt
• plural: liegen

Because in German compounds, the first noun usually appears in a basic stem form without its own article.

So instead of saying something like Rolle des Garns in everyday German, you usually get the compact compound:

• Garnrolle = thread spool / spool of thread

This is normal in German. The relationship between the parts is built into the compound itself.