
die Befestigung
attachment
The process of fixing or fastening something in place.
Die Befestigung des Regals an der Wand dauerte eine Stunde.
Attaching the shelf to the wall took an hour.
attachment / fortification / fastener
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attachment
The process of fixing or fastening something in place.
Die Befestigung des Regals an der Wand dauerte eine Stunde.
Attaching the shelf to the wall took an hour.

fortification
A structure built to defend a place, such as a fortress, wall, or rampart.
Die alte Stadtmauer ist eine beeindruckende Befestigung aus dem Mittelalter.
The old city wall is an impressive fortification from the Middle Ages.

fastener
An object or device used to fasten something, for example a screw or a clamp.
Im Baumarkt finden Sie die passende Befestigung für Ihr Bild.
At the hardware store, you will find the right fastener for your picture.
'Die Befestigung' (attachment / fortification / fastener) is the noun related to the verb 'befestigen' (to fasten). Depending on the context, it can refer to the process of fastening, the result (a fortress), or the tool used for it (a screw).
Wir müssen das Zelt gut befestigen, damit es der Wind nicht wegweht.
We have to secure the tent well so the wind doesn't blow it away.
The meaning becomes clear from the context. If people are talking about a 'Schraube' (screw) or a 'Dübel' (wall plug/anchor), an object is meant. If it is about a 'Burg' (castle) or 'Mauer' (wall), a defensive structure is meant. If an action is being described, such as '... des Spiegels' (... of the mirror), the process is meant.
Für diese schwere Lampe brauchen wir eine spezielle Befestigung.
For this heavy lamp, we need a special fastener.
When the process of fastening is being described, the preposition 'an' with the dative often follows to indicate the location. The structure is: die Befestigung von etwas an etwas (the attachment of something to something).
Die Befestigung der Kamera an der Decke war kompliziert.
Attaching the camera to the ceiling was complicated.
When an object is meant, the word is often combined with verbs like 'kaufen' (to buy), 'suchen' (to look for), 'finden' (to find), or 'brauchen' (to need). In that case, people are talking about screws, wall plugs/anchors, hooks, or clamps.
Im Baumarkt habe ich die passenden Befestigungen für das Bild gefunden.
At the hardware store, I found the right fasteners for the picture.
anchoring
Befestigung is the general term for fixing or fastening an object in place. Verankerung specifically refers to a stable fastening on or in a solid base. Befestigung fits a simple connection, while Verankerung is more appropriate for a secure connection to the base.

Die Befestigung des Kabels am Gestell erfolgt mit einer Klemme.
The cable is attached to the frame with a clamp.
Die Verankerung des Gestells im Betonboden erfolgt mit stabilen Bolzen.
The frame is anchored in the concrete floor with sturdy bolts.