Ich befestige die Einladungskarte mit einer Heftklammer an der Mappe.

Befestige comes from the verb befestigen, which means to attach, to fasten, or to secure.

In this sentence, ich befestige is:

• 1st person singular
• present tense

So it means I attach / I am attaching / I fasten.

Because German verbs have to be conjugated to match the subject.

The infinitive is befestigen = to attach.

With ich, the present tense ending is usually -e:

• ich befestige
• du befestigst
• er/sie/es befestigt
• wir befestigen
• ihr befestigt
• sie/Sie befestigen

So ich befestige is the correct form for I attach.

Die Einladungskarte is the direct object of the sentence — it is the thing being attached.

The noun Einladungskarte is feminine, so its nominative singular article is die.
In the accusative singular, feminine nouns still use die, so the article does not change:

• nominative: die Einladungskarte
• accusative: die Einladungskarte

So even though it is the object, it still appears as die Einladungskarte.

It is a compound noun:

• Einladung = invitation
• Karte = card

So Einladungskarte means invitation card.

German very often combines nouns like this into one word.

Because the preposition mit always takes the dative case.

The noun Heftklammer is feminine, so:

• nominative: eine Heftklammer
• dative: einer Heftklammer

That is why the sentence has mit einer Heftklammer = with a staple.

Usually, Heftklammer means staple, not paper clip.

That is a very common confusion for English speakers.

Compare:

• die Heftklammer = staple
• die Büroklammer = paper clip

So this sentence is talking about attaching the card with a staple.

This is a very common question.

Here, an is followed by the dative: an der Mappe.

With befestigen, German commonly uses an + dative for the thing something is attached to:

• etwas an der Wand befestigen
• etwas am Rucksack befestigen
• etwas an der Mappe befestigen

So in this sentence, der Mappe is dative because of the preposition an in this construction.

A useful way to learn it is:

• etwas an etwas befestigen often uses dative for the second noun.

Mappe usually means something like:

• folder
• file
• portfolio

It does not mean map in the English sense. That is a false friend.

So an der Mappe means to the folder / on the folder, depending on context.

Because they describe two different relationships:

• mit einer Heftklammer = with a staple
  → this tells you the means/tool
• an der Mappe = to/on the folder
  → this tells you where / to what the card is attached

So the sentence separates:

1. what is being attached → die Einladungskarte
2. how → mit einer Heftklammer
3. to what → an der Mappe

German word order is somewhat flexible, but not completely free.

This sentence has a very natural neutral order:

• Ich = subject
• befestige = verb
• die Einladungskarte = direct object
• mit einer Heftklammer = means
• an der Mappe = location/attachment target

You could also change it for emphasis, for example:

• Mit einer Heftklammer befestige ich die Einladungskarte an der Mappe.
• An der Mappe befestige ich die Einladungskarte mit einer Heftklammer.

But the original version sounds like a normal, straightforward statement.

Yes. A more colloquial alternative is:

Ich mache die Einladungskarte mit einer Heftklammer an der Mappe fest.

Here, festmachen or ... fest machen can mean to fasten / attach.

Compared with befestigen:

• befestigen sounds a bit more formal or neutral
• festmachen / festmachen an can sound more everyday

Both are understandable, but befestigen is a very good standard verb to know.

Because articles in German carry important grammar information such as:

• gender
• case
• number

In this sentence:

• die Einladungskarte → feminine, accusative singular
• einer Heftklammer → feminine, dative singular
• der Mappe → feminine, dative singular

So the articles are doing a lot of grammatical work. They help show how each noun functions in the sentence.

No. Befestigen is not separable.

So you say:

• Ich befestige die Karte.
• Er befestigt das Schild.

The verb stays together.

This is different from separable verbs like:

• anmachen
• aufhängen
• festmachen

For example:

• Ich hänge das Bild auf.
• Ich mache die Karte fest.

But:

• Ich befestige die Karte. ✅
• Ich festige die Karte be... ❌

So you should learn befestigen as one complete, inseparable verb.