My best guess here is that you really mean the 10 second backcourt count. It begins when there is team control on the floor. Team control is established when a player establishes player control. Player control is defined as a player holding or dribbling a ball inbounds.
So, if you really mean the 10 second backcourt count, it starts when an offensive player on the floor receives (not just touches, as in a deflection) the ball and is in that team's backcourt.
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Yom HaShoah
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