Episode 162- I saw her
To summarize everything again. The letter Aernest was referring to was one sent to announce Aernest, Eugene, and Euria's affirmation into the Xenperia Academy.
When Emperor Zen took the throne, he made attending school mandatory for every child. So as of the present, it is obligatory for all citizens of Xenperia, nobles or commoners, males or females, to have a basic education. It is possible to delay attending school however, the maximum age you can delay it too was 10. If you are 10 and you are not yet attending school, knights would make rounds to your house and forcefully bring you to school.
"Wait! Wait! Wait!" Eugene didn't say anything yet when Aernest raised his voice. "Before choosing subjects! Where will you be living sister?" His face was filled with expectations as he looked at her.