to admit
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to admit
To reluctantly admit that something is true, especially one's own mistake, weakness, or guilt.
Er musste sich eingestehen, dass er einen großen Fehler gemacht hatte.
He had to admit to himself that he had made a big mistake.
'Eingestehen' (to admit) is a separable verb with the prefix 'ein-'. In a main clause, the prefix comes at the end. The verb is irregular: gesteht ein, gestand ein, hat eingestanden.
Nur widerwillig gestand er seinen Irrtum ein.
Only reluctantly did he admit his mistake.
'Eingestehen' (to admit) can be used reflexively ('sich etwas eingestehen' — to admit something to oneself), with an accusative object ('einen Fehler eingestehen' — to admit a mistake), or with a 'dass' clause.
Ich muss mir eingestehen, dass ich Hilfe brauche.
I have to admit to myself that I need help.
People typically admit negative things. Common combinations are: 'einen Fehler eingestehen' (to admit a mistake), 'eine Schwäche eingestehen' (to admit a weakness), 'seine Schuld eingestehen' (to admit one's guilt), or 'eine Niederlage eingestehen' (to admit defeat).
Es fällt ihm schwer, seine eigene Schwäche einzugestehen.
He finds it difficult to admit his own weakness.
to recognize / acknowledge
'anerkennen' and 'eingestehen' can both mean admitting that something true is the case. 'eingestehen' is used especially for one's own mistakes, weaknesses, or guilt. It often sounds as if the admission is difficult. 'anerkennen' is broader: you can also acknowledge a fact, a problem, or another person's opinion. When it is about a personal mistake, 'eingestehen' is often more precise; when it is more generally about accepting a truth, 'anerkennen' fits better.
Am Abend gesteht Paul ein, dass er den Termin vergessen hat.
In the evening, Paul admits that he forgot the appointment.
Meine Schwester hat anerkannt, dass die Aufgabe schwieriger war als gedacht.
My sister acknowledged that the task was more difficult than expected.