Question

after the autumnal equinox, more light begins to fall on the
hemisphere and reaches maximum sunlight about
(date)

Explanation:

After the autumnal equinox (around September 22 - 23), the Southern Hemisphere starts receiving more sunlight. The maximum sunlight for the Southern Hemisphere is reached around the summer solstice (December 21 - 22). So the first blank is "Southern" and the second blank is "December 21 (or 22)".

Answer:

First blank: Southern
Second blank: December 21 (or 22)