Suppose you live at a mid-latitude in the southern hemisphere (such as in australia, new zealand, chile, or south africa). when will you have 12 hours of daylight and 12 hours of darkness?

The next 2 equinoxes will happen Sept 22, 2017 and March 20, 2018. The spring and autumn equinoxes are when you have an equal number of hours of daylight and darkness. It doesn't matter what hemisphere you live in, the event happens at the same time, generally close to Sept 22nd and March 20th of each year. The next spring equinox for the southern hemisphere will be happening Friday, September 22, 2017 at 20:02 UTC. The next Fall equinox will happen Tuesday, March 20, 2018 at 16:15 UTC.