Bitte pass auf die Stecknadel auf, sie liegt neben dem Papier.

Because this uses the separable verb aufpassen plus the preposition auf.

• aufpassen = to watch out / be careful / pay attention
• auf etwas aufpassen = to watch out for something / be careful with something

In a main clause, the separable prefix goes to the end:

• Ich passe auf.
• Pass auf!

If you add the thing you are watching out for, it goes in the middle:

• Pass auf die Stecknadel auf.

So the first auf belongs to the object phrase auf die Stecknadel, and the second auf is the separated prefix of aufpassen.

Pass is the informal singular imperative, used when speaking to one person as du.

The verb is aufpassen. The du imperative is:

• Pass auf! = Watch out! / Be careful!

Compare:

• du passt auf = you watch out
• Pass auf! = watch out!

Other forms would be:

• Passt auf! = plural you all
• Passen Sie auf! = formal you

So Bitte pass auf ... auf is addressing one person informally.

It is in the accusative, because aufpassen auf takes auf + accusative.

So the structure is:

• auf die Stecknadel auf

With a feminine noun like die Stecknadel, the article is die in both nominative and accusative, so you do not see a change.

A clearer example with a masculine noun would be:

• Pass auf den Hund auf.

There, den Hund clearly shows the accusative.

Stecknadel usually means a straight pin or sewing pin.

It is a compound noun:

• stecken = to stick / insert
• Nadel = needle

So it is literally something like a sticking needle, but the natural English meaning is pin.

German uses grammatical gender, so nouns are referred to with pronouns that match their grammatical gender.

• die Stecknadel is feminine
• so the pronoun is sie

In English, you would say it, but in German the noun’s gender controls the pronoun:

• Die Stecknadel ist klein. Sie liegt neben dem Papier.

Also, this sie is lowercase because it means she/it here, not the formal you (Sie).

German often uses a more specific position verb where English might simply use is.

• liegen = to lie, to be lying, to be located in a lying/resting position

For objects resting on a surface, liegen is very natural:

• Die Stecknadel liegt neben dem Papier.

Using ist is not impossible in some contexts, but liegt sounds more idiomatic and more precise here, because the pin is physically lying there.

German often distinguishes:

• liegen for things lying
• stehen for things standing upright
• sitzen for beings or things in a sitting/fitted position

Because neben is a two-way preposition.

• It takes the dative for location
• It takes the accusative for movement toward a place

Here, the pin is already located next to the paper, so this is location, not movement:

• neben dem Papier = next to the paper

Compare:

• Die Stecknadel liegt neben dem Papier. = location
• Ich lege die Stecknadel neben das Papier. = movement/placement

The noun Papier is neuter:

• das Papier

After neben in a location meaning, you need dative, so:

• das Papier → dem Papier

So:

• nominative: das Papier
• dative: dem Papier

In this sentence, it most naturally means watch out for the pin or be careful with the pin.

The verb aufpassen auf can sometimes mean keep an eye on or look after, depending on context. But here, because the second clause says where the pin is, the idea is clearly a warning:

• Be careful, there’s a pin next to the paper.

So the sense is not really look after the pin, but rather don’t miss it / don’t touch it carelessly / don’t get pricked.

The sentence contains two main clauses:

• Bitte pass auf die Stecknadel auf
• sie liegt neben dem Papier

German can link short, closely connected main clauses with a comma, especially in natural, spoken-style language.

It is a bit like saying:

• Please watch out for the pin, it’s next to the paper.

You could also say:

• Bitte pass auf die Stecknadel auf, denn sie liegt neben dem Papier.

But the original version is perfectly natural.

Because aufpassen is a separable verb.

In its dictionary form, it is written as one word:

• aufpassen

But in a main clause, the prefix separates:

• Ich passe auf.
• Du passt auf.
• Pass auf!

When extra information appears, it goes between the verb stem and the separated prefix:

• Pass auf die Stecknadel auf.

This is a very common pattern in German with separable verbs, such as:

• anrufen → Ich rufe dich an.
• einkaufen → Wir kaufen heute ein.