We had an under counter B&D drip coffee maker many, many years ago. It had two brackets on the side of the coffee maker that screwed into the bottom of the cabinet and the coffee maker hung from the bracket. There was a catch on the bracket that released the coffee maker, and it slide forward (on the bracket - rail - track). Once the coffee maker is off the track, the screws that held up under the cabinet could be removed. Of course, installing was just the opposite. Attach the bracket-track first, then slide the coffee maker in until the clip catch caught it. Maybe yours is the same way. Look, feel, for a catch that releases the coffee maker from the track holding it in.
