abmachen
to agree
To discuss something with one or more people and establish it as binding.
Wir haben abgemacht, dass wir uns morgen um 10 Uhr treffen.
We agreed that we would meet tomorrow at 10 o'clock.

to agree / remove
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to agree
To discuss something with one or more people and establish it as binding.
Wir haben abgemacht, dass wir uns morgen um 10 Uhr treffen.
We agreed that we would meet tomorrow at 10 o'clock.

'Abmachen' (to agree / remove) is a separable verb. The prefix 'ab-' comes at the end in a main clause; in subordinate clauses the verb stays together, and in the infinitive with 'zu', 'zu' stands between 'ab' and 'machen'.
Wir machen für morgen einen Termin ab.
We arrange an appointment for tomorrow.
You can recognize the meaning from the context: if it is about an agreement between people, 'vereinbaren' (to agree/arrange) is meant. If an object is detached from another object, it means 'entfernen' (to remove). The expression 'mit sich selbst abmachen' means 'entscheiden' (to decide).
Die beiden Firmen haben einen neuen Vertrag abgemacht.
The two companies agreed on a new contract.
When you want to express what was agreed, you often use a subordinate clause with 'dass' or an infinitive construction with 'zu'.
Wir haben abgemacht, dass jeder die Hälfte bezahlt.
We agreed that everyone would pay half.
When you remove something, the surface it is removed from is introduced with the preposition 'von' and the dative.
Er macht das Kaugummi von seiner Schuhsohle ab.
He removes the chewing gum from the sole of his shoe.
The meaning 'to decide for oneself' is used almost exclusively in the fixed expression 'etwas mit sich (selbst) abmachen' (to decide something for oneself). The pronoun 'sich' is necessary here.
Diese Entscheidung muss jeder mit sich selbst abmachen.
Everyone has to make this decision for themselves.
to remove
'entfernen' and 'abmachen' can both mean that you take something away. 'entfernen' sounds more general and often a bit more neutral or precise, especially when something is to be gotten rid of. 'abmachen' is mainly used when something is attached to something else and you detach it, for example a price tag, a picture, or a lid. 'abmachen' is also very common in everyday language. If the attachment is important, 'abmachen' sounds more natural. If it is generally about taking something away or getting rid of it, 'entfernen' fits better.

Vor dem Waschen macht er das Namensschild von der Jacke ab.
Before washing it, he takes the name tag off the jacket.
Bitte entfernen Sie die Datei vom Computer, wenn Sie sie nicht mehr brauchen.
Please remove the file from the computer if you no longer need it.