What mode is not permitted with a flight director or autopilot during an approach?

The correct choice identifies that Speed Mode is not permitted with a flight director or autopilot during an approach. During an approach, the focus is typically on controlling the aircraft's altitude, maintaining the correct flight path, and adhering to specific glide slope and localizer signals for landing. Speed Mode, which allows the autopilot to control the aircraft's speed independently, could conflict with these critical parameters, potentially leading to deviations from the required approach path or glide slope.

In contrast, Altitude Hold Mode allows the aircraft to maintain a specific altitude, which can be essential during certain phases of an approach as pilots prepare for descent. Bank Angle Mode can also be used to maintain specific bank angles, which can aid in managing the aircraft's path during turns, including in an approach scenario, provided that it is appropriate to the situation. Approach Mode is specifically designed for the landing phase, enabling the autopilot to execute the glide slope capture and facilitate safe landings. Therefore, Speed Mode is the one mode that does not align with the critical needs for safe and precise approach operations.