eindrücken
to dent
To cause an indentation or dent in a surface by applying pressure.
Der Hagelsturm hat das Dach des Autos an mehreren Stellen eingedrückt.
The hailstorm dented the roof of the car in several places.

to dent / force in
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to dent
To cause an indentation or dent in a surface by applying pressure.
Der Hagelsturm hat das Dach des Autos an mehreren Stellen eingedrückt.
The hailstorm dented the roof of the car in several places.

'Eindrücken' (to dent / force in) is a separable verb. The prefix 'ein-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Der Stein drückte eine Delle in die Motorhaube ein.
The stone dented the hood.
The verb is made up of the prefix 'ein-' (in, into) and the verb 'drücken' (to press). So the meaning is literal: to press something inward.
Drück den Knopf vorsichtig ein, um das Gerät zu starten.
Press the button in carefully to start the device.
The difference in meaning becomes clear from the object. If it refers to a surface (roof, sheet metal, can), it means 'to make a dent'. If it refers to an entryway (door, window), it means 'to open by force'.
Der fallende Ast hat das Garagentor eingedrückt.
The falling branch dented the garage door.
to press / hug
'drücken' and 'eindrücken' both have to do with pressure. 'drücken' is more general: you press a button, a key, or a surface. Nothing has to break or change its shape. 'eindrücken' means that pressure causes something to go inward, for example creating a dent, or that something is forced inward violently. The words can be confused because both describe movement caused by pressure. The important point is: 'drücken' describes the action, while 'eindrücken' usually describes the result or the force of the pressure.

Mein Bruder hat am Abend aus Versehen die dünne Tür eingedrückt.
In the evening, my brother accidentally dented the thin door.
Im Büro drückt der Lehrer auf den Knopf des Kopierers.
In the office, the teacher presses the button on the copier.