What is the phase of the Moon when the Sun is on the meridian and the Moon is just at the horizon?

I don't think this is a trick question! If the Sun were at the meridian ( local noon time) then depending on your latitude and whether you had a clear flat view of the true horizon, the phase would be either something between New Moon and First Quarter if it was on the eastern horizon, or Last Quarter and New Moon if it was on the western horizon. It would be about 1/2 of its fully illuminated phase.