One of the current questions in Babylonian astronomy is how the Babylonians were able to find and agree on the length of lunar months. Another question is how the days of the four full-moon observations and the last visibility of the old moon were predicted. This paper shall show how the days of each of the Lunar Six, i.e., the days of each of the six special lunar phases observed by the Babylonians, can be found easily. The days of the Lunar Six are interdependent and rather difficult to determine by means of modern astronomical considerations. But a detail in the Babylonian Goal-Year method for predicting the values of the Lunar Six gives the clue for finding the days: is the normal Goal-Year method utilized, all days will remain the same as they were one Saros earlier – if the Goal-Year method needs corrections, then the day of the corresponding phenomena will be displaced by one day. This means that if one knows the values and days of all Lunar Six for one month (plus some values found six months earlier), then one can find the values and days for all the Lunar Six to come one Saros later by means of the Goal-Year method; particularly the day of the NAN. This day (30 or 31), at which the first of the Lunar Six occurs, indicates the length of the previous month. Therefore, evidently, this reconstructed method also gives easy means for finding – and agreeing on – the lengths of months to come.