Eckersley pitched Bates to an 0–2 ball–strike count when he hit the ball weakly to the third baseman and beat out an infield single; it was Bates' first hit against a right-handed pitcher in his MLB career.
The situation described is about Eckersley pitching to Bates with a 0-2 count, Bates hitting a weakly-hit ground ball to the third baseman for an infield single, and Bates achieving his first hit against a right-handed pitcher during his MLB career.