sich versöhnen
to make up
To make peace again and get along after an argument or disagreement.
Nach dem langen Streit haben sich die beiden Schwestern endlich wieder versöhnt.
After the long argument, the two sisters finally made up again.

to reconcile
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to make up
To make peace again and get along after an argument or disagreement.
Nach dem langen Streit haben sich die beiden Schwestern endlich wieder versöhnt.
After the long argument, the two sisters finally made up again.

The prefix 'ver-' in 'versöhnen' (to reconcile) is inseparable. It remains directly at the beginning of the verb in all sentence forms and tenses.
Er versöhnte sich schnell wieder mit seinem Freund.
He quickly made up with his friend again.
You can recognize the meaning of 'versöhnen' (to reconcile) from the grammar. 'Sich versöhnen' means to make peace. 'Jemanden mit etwas versöhnen' means to make someone accept a situation. 'Jemanden mit jemandem versöhnen' means to mediate between people.
Die Geschwister haben sich versöhnt.
The siblings made up.
In the meaning 'to make peace', the verb is always used reflexively: 'sich versöhnen' (to make up). When several people are involved, you can also add 'miteinander' (with each other) to emphasize reciprocity.
Das Paar hat sich nach dem Streit wieder versöhnt.
The couple made up again after the argument.
The structure is 'etwas versöhnt jemanden mit etwas' (something reconciles someone to something). The subject is often a positive experience that allows a person (accusative) to make peace with a negative situation (mit + dative).
Der überraschende Sieg versöhnte die Mannschaft mit dem harten Training.
The surprising victory reconciled the team to the hard training.
When a person acts as a mediator, that person is the subject of the sentence. The parties in conflict are the objects. The structure is: 'Person A versöhnt Person B mit Person C' (Person A reconciles Person B with Person C).
Ein guter Freund hat versucht, mich mit meinem Bruder zu versöhnen.
A good friend tried to reconcile me with my brother.
to accept
'akzeptieren' and 'versöhnen' can both mean that you no longer fight against a difficult or unpleasant situation. 'akzeptieren' is more neutral: you acknowledge that something is the way it is, even if you do not like it. 'versöhnen' moves more toward inner peace. You have not only understood that something is the way it is, but you cope with it better emotionally. That is why 'akzeptieren' often fits facts or rules, while 'sich mit etwas versöhnen' sounds more natural when feelings and personal disappointment play a role.

Nach einigen Wochen hat sich Tom mit dem Umzug in die kleine Wohnung versöhnt.
After a few weeks, Tom has come to terms with moving into the small apartment.
Ihr akzeptiert den neuen Termin, obwohl er nicht ideal ist.
You accept the new appointment, even though it is not ideal.