When do we experience in Australia our shortest days and longest nights?why?

The longest days in Australia should be expected between 21st and 23rd December, while the shortest day should be expected around June 21st. That is because the summer hemisphere the summer solstice happens around 22nd of December, and winter solstice happens around June 21st.

Explanation:

Australia is in the southern hemisphere, and that is why summer starts in December, and winter starts in June. All the countries in the northern hemisphere, for example United States are totally different, because the summer starts starts in June, and winter in December. The sun is at the highest point in December and covers Australia the most.