jemandem etwas vorwerfen
to accuse someone of something
To criticize or accuse someone for misconduct or for failing to do something.
Er warf ihr vor, sein Vertrauen missbraucht zu haben.
He accused her of having abused his trust.

to accuse / throw forward
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to accuse someone of something
To criticize or accuse someone for misconduct or for failing to do something.
Er warf ihr vor, sein Vertrauen missbraucht zu haben.
He accused her of having abused his trust.

'Vorwerfen' (to accuse / to throw forward) is a separable verb. The prefix 'vor-' comes at the end in a main clause. In subordinate clauses and in the infinitive with 'zu', the verb stays together.
Sie wirft ihm seine Unpünktlichkeit vor.
She accuses him of being unpunctual.
The verb consists of 'vor' (forward/in front) and 'werfen' (to throw). The literal meaning is 'to throw forward'. The figurative meaning 'to accuse' can be imagined as throwing an accusation 'at someone's feet'.
Der Hund wirft beim Laufen die Beine weit vor.
The dog throws its legs far forward when running.
When accusing someone, the verb has a fixed structure: the person being accused is in the dative. The thing they are accused of is in the accusative.
Der Chef warf dem Mitarbeiter (Dativ) einen schweren Fehler (Akkusativ) vor.
The boss accused the employee (dative) of a serious mistake (accusative).
The literal meaning 'nach vorne werfen' (to throw forward) is rare. It is mainly used in sports (e.g., handball) or to describe animal movements. In most other contexts, 'vorwerfen' means to accuse.
Der Handballspieler wirft den Ball schnell vor zum Mitspieler.
The handball player quickly throws the ball forward to his teammate.
to throw
'werfen' and 'vorwerfen' can both describe a forward movement with the hand. 'werfen' is the normal word when you throw a ball, a stone, or another object through the air. 'vorwerfen' can also mean to throw something forward, but in this sense it is more specific. Much more often, 'jemandem etwas vorwerfen' means that you blame someone or criticize them. That is why the words are easy to confuse: the prefix 'vor-' often turns the normal action into a reproach in a figurative sense. For the simple movement, you usually use 'werfen'.

Der Lehrer wirft ihr vor, dass sie in der Pause das Heft eines Mitschülers versteckt hat.
The teacher accuses her of having hidden a classmate's notebook during the break.
Nach der Arbeit wirft sie den Ball für ihren Hund in den Garten.
After work, she throws the ball into the garden for her dog.