Astronomy wizard required for calculation

Hi. I've got a flat lawn (horizontal) and at the end of the lawn a
perpendicular wall. In front of the lawn and wall is my house and during
winter the sun fails to shine on the wall and lawn.

Assume the house ridge runs east and west.

The wall is not quite east and west, but I want to discover at what day
and month the sun shines at the intersection of lawn and the wall at the
mid point of the wall.

Right now the sun shines onto the lawn at noon. Of course as the sun
gets lower afer summer solstice the shadow line starts to move down the
lawn and up the wall.

If I measure the distance from the wall/lawn interection and the
shadow-line at noontime sometime this week - and post it here - can it
be determined at what day and month the shadow line rests at the
wall/lawn intersection - at noontime? Of course there will be two
times, one in spring, and one in fall.

I cannot do the calculation. Easy peasy for and astronomer. Right? :c)

Thanks.