Which flight director lateral mode arms vertical guidance?

The flight director lateral mode that arms vertical guidance is the approach mode, commonly referred to as APPR. This mode is specifically designed for precision approaches where both lateral and vertical guidance are required to safely land an aircraft. When engaged, APPR mode utilizes the signals from an Instrument Landing System (ILS) to provide both lateral (localizer) and vertical (glideslope) information, ensuring pilots can effectively navigate during the final stages of landing.

In contrast, the VNAV mode is focused on vertical navigation for climb and descent profiles without the precision landing aspect. The NAV mode generally provides lateral navigation routing but does not engage vertical guidance on its own. The PTCH mode refers specifically to pitch control, which is unrelated to lateral guidance aspects. The APPR mode is thus the key to enabling vertical guidance while in a lateral approach context, making it the correct choice for this question.