You might be referring to the 16 yard/15 metre hit, which is a free hit taken by the defense if an attacker plays the ball over the backline, taken in line with where it went out, parallel to the sideline and up to 16 yards/15 metres from the backline.
The hit out may also refer to the process of beginning play in a penalty corner, normally called the injection; if the ball is hit into the field, it may be called a hit-out. If pushed, it may be called a push-out.
Otherwise, some people refer to the centrepass - the free hit that starts or restarts a game after goals or halftime - as a hit-off. Both of these are usually called by their names; the centrepass or the "16"/"16 yard".
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In Field Hockey, the hit is a method of striking the ball hard using a swinging motion of the stick, and is often used when pure power is desired, such as for shots on goal, free hits or driving the ball downfield.
In Ice Hockey, the hit is the event of using the body to charge another player, striking their body with your own, and is used to remove them from controlling the puck.