Here, in our planetarium, we often say that the Moon is running
  on the Sun's path, 6 months later.
  summer : Sun's high, Moon's down
  winter : Sun's down, Moon's high in the sky;

  It's an easy, but not too wrong tip for non-astronomical public.

It may not be "too wrong", but it is wrong.  I'm not talking about the few degrees tilt of the plane of the Moon's orbit.  Even ignoring that, your statement is only true for the full moon.  At new moon, for example, the Moon is running on the current path of the sun, not that delayed by six months.  Psychologically, it makes some sense, since we care less about the moon when it is "small" and when it is being out-shined by the sun.  And you certainly run a risk of losing your public if you try to explain too much.  But my nit-picking mind would be more comfortable if you would at least change "Moon" to "full Moon" (the restriction to be immediately forgotten by 99.9% of the public).

--Art Carlson

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