Die Mitarbeiterin befestigt den Kofferanhänger am Koffer.

Mitarbeiterin is the feminine form of Mitarbeiter. The ending -in often makes a noun specifically female in German.

• der Mitarbeiter = male employee / employee
• die Mitarbeiterin = female employee

The article die matches the feminine noun Mitarbeiterin.

The verb is befestigen. In the present tense, with a third-person singular subject such as die Mitarbeiterin, it becomes befestigt.

Present tense:

• ich befestige
• du befestigst
• er/sie/es befestigt

So Die Mitarbeiterin befestigt ... means the subject is she or the female employee, and the verb takes the -t ending.

Because it is the direct object of the verb befestigen.

The employee is attaching what?
→ den Kofferanhänger

That makes Kofferanhänger the thing directly affected by the action, so it takes the accusative case.

Since Kofferanhänger is masculine, its article changes like this:

• nominative: der Kofferanhänger
• accusative: den Kofferanhänger

Am is a contraction of an dem, and dem is dative.

Here, an is being used to show where the luggage tag is attached: on/at the suitcase. This is treated as a location or position, so German uses dative here:

• an dem Koffer → am Koffer

If you used an den Koffer, that would be accusative, which often suggests movement toward something. In this sentence, German normally uses am Koffer with befestigen to express the attachment point.

Am is just a shortened form of an dem.

This kind of contraction is very common in German:

• an dem → am
• in dem → im
• zu dem → zum
• zu der → zur

So am Koffer literally comes from an dem Koffer.

With compound nouns in German, the last part decides the grammatical gender.

• Koffer = suitcase
• Anhänger = tag, pendant, trailer, attachment

The final part is Anhänger, which is masculine: der Anhänger.
So the whole compound is also masculine: der Kofferanhänger.

That is why you get:

• nominative: der Kofferanhänger
• accusative: den Kofferanhänger

German very often combines nouns into a single compound noun.

So instead of writing something like suitcase tag as two separate words, German makes one word:

• Koffer
  • Anhänger = Kofferanhänger

This is completely normal in German. The last element is the main noun, and the earlier part describes it.

In German, all nouns are capitalized, not just proper names.

So in this sentence:

• Mitarbeiterin
• Kofferanhänger
• Koffer

all begin with capital letters because they are nouns.

In this sentence, it is present tense: attaches / is attaching.

It is true that befestigt can also be the past participle of befestigen, but in that case German would normally need an auxiliary verb such as:

• hat befestigt

Since there is no auxiliary here, and the verb is in second position after the subject, this sentence is understood as present tense.

German main clauses usually follow the verb-second rule: the finite verb comes in the second position.

Here the sentence begins with the subject:

• Die Mitarbeiterin | befestigt | den Kofferanhänger am Koffer.

So:

1. first position = Die Mitarbeiterin
2. second position = befestigt

This is one of the most important word-order rules in German.

Yes, that is grammatically possible, but it is less neutral.

German allows some flexibility with word order, especially with objects and prepositional phrases. However, the most natural neutral order here is:

Die Mitarbeiterin befestigt den Kofferanhänger am Koffer.

Putting am Koffer earlier can shift emphasis toward the suitcase or the location of attachment.

They are two different nouns with different roles:

• der Koffer = the suitcase
• der Kofferanhänger = the luggage tag

The suitcase is the item the tag is attached to, while the luggage tag is the item being attached.

Grammatically:

• den Kofferanhänger = direct object, accusative
• am Koffer = prepositional phrase, dative

German often expresses this idea with a preposition + case rather than matching English word-for-word.

English says:

• attach the tag to the suitcase

German says:

• den Kofferanhänger am Koffer befestigen

Here am Koffer covers the idea of where the tag ends up attached. So the structure is different from English, even though the meaning is the same.