The noon Sun on January 21, as viewed from Binghamton, was at 4) between position 2 and position 3 .Therefore , 4) between position 2 and position 3 is correct .
This is because the winter solstice, which is the shortest day of the year, occurs on or around January 21.
On the day of the winter solstice, the Sun is at its lowest point in the sky in the Northern Hemisphere.
This means that the Sun will appear to be at position 3 on the diagram you provided.
Another way to think about it is that the Sun is directly overhead the equator at noon on the day of the winter solstice.
Binghamton is located in the Northern Hemisphere, so the Sun will appear to be south of directly overhead at noon on January 21.
This corresponds to position 3 on the diagram.
Why is this the answer?
The diagram shows the position of the Sun at noon on the summer solstice (June 21), the autumnal equinox (September 23), and the winter solstice (December 21).
The Sun is at its highest point in the sky on the summer solstice, so it appears to be at position 1 on the diagram.
The Sun is at its lowest point in the sky on the winter solstice, so it appears to be at position 3 on the diagram.
The Sun is at an intermediate position on the autumnal equinox, so it appears to be at position 2 on the diagram.
Binghamton is located in the Northern Hemisphere, so the Sun will always appear to be south of directly overhead at noon.
This means that the Sun will always appear to be between position 2 and position 3 on the diagram, as seen from Binghamton.
Therefore, the noon Sun on January 21, as viewed from Binghamton, was at position 3.