zurückhalten
to hold back
To physically prevent someone or something from moving forward or leaving.
Die Polizei musste die aufgeregte Menge zurückhalten.
The police had to hold back the excited crowd.

to hold back / withhold
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to hold back
To physically prevent someone or something from moving forward or leaving.
Die Polizei musste die aufgeregte Menge zurückhalten.
The police had to hold back the excited crowd.

'Zurückhalten' (to hold back/withhold) is a separable verb. The prefix 'zurück-' goes to the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Er hielt den Hund an der Leine zurück.
He held the dog back on the leash.
The verb consists of 'zurück' (back) and 'halten' (to hold). The literal meaning 'to hold back' or 'to prevent from moving forward' is the basis for all figurative meanings, such as holding back feelings or withholding money.
Die Sicherheitskräfte hielten die Fans zurück.
The security forces held the fans back.
In the meaning 'to behave modestly', the verb is always used reflexively with 'sich' in the accusative. It describes a conscious decision not to become active or attract attention.
Normalerweise ist sie sehr gesprächig, aber heute hält sie sich zurück.
Normally she is very talkative, but today she is holding back.
When the idea is not expressing something, 'zurückhalten' (to hold back) is often combined with abstract nouns such as 'Informationen' (information), 'Meinung' (opinion), 'Gefühle' (feelings), 'Wut' (anger), or 'Tränen' (tears).
Er konnte ein Lachen kaum zurückhalten.
He could hardly hold back a laugh.
The exact meaning often depends on the object. If it is a person or an animal, the physical meaning is intended. With abstract things like 'Meinung' (opinion) or 'Gefühl' (feeling), it is about not expressing something. With 'Geld' (money) or 'Zahlung' (payment), it is about withholding.
Sie hielt ihren Sohn am Arm zurück.
She held her son back by the arm.
to publish
'veröffentlichen' and 'zurückhalten' are opposites here. 'veröffentlichen' means that information or a work is made available to the public. With information, 'zurückhalten' means that you deliberately do not say it, show it, or pass it on. So the difference is: with 'veröffentlichen', others are supposed to find something out; with 'zurückhalten', it stays with the person or organization that has the information. This is especially important with news, reports, or official announcements.

Die Kundin hält wichtige Informationen zurück, weil sie noch unsicher ist.
The customer is withholding important information because she is still unsure.
Am Montag veröffentlicht die Firma die Ergebnisse des Projekts.
On Monday, the company will publish the results of the project.