There is no exact date when you conceived - not that can be pinpointed after the fact. A due date is an estimation and if you don't know when your last period was it makes it harder to figure out (I'm assuming you don't, because calculating your conception date would be easier that way).

Generally a woman ovulates 2 weeks before her next period. If you have a classic 28 day cycle (not all women do), and are very regular, you can generally expect to ovulate on day 14 of your cycle. But we don't know these things about you so we can only guess.

In this case, June 12 is a potential conception date. That would mean your last period was on or around May 29.