At point D, you indicated that the direction of the angular velocity is 8. If this is true, then the axis of rotation of the ball lies along the line connecting directions 4 and 8. Is this really true?

The direction of an angular velocity points along the rotational axis of a rotating object. Unfortunately, the rotation axis points in two opposite directions. The right hand rule is used to select which of these two directions corresponds to the direction of the angular velocity. With your right hand, grab the rotational axis of the ball so that your fingers wrap around the axis in the direction that the ball is rotating. With your hand in this position, your thumb points in the direction of the angular velocity. The diagrams below illustrate balls with angular velocities directed out of the page and into the page.