The moon which you can see on the 15th is called “Chushu-no-meigetsu” which means “Mid-Autumn moon”. In English, it is called “Harvest moon”
It is also called “Potato moon” because people offer taro, a kind of potato, to the moon.
Actually Potato also has Penis means at that time..
So she is having his potato while seeing the Potato moon..
Neya no hinagata