@Nunally What sort of educatiom teaches you how to conquer another country? Generally speaking no single person would even need to know it because it's a massive undertaking with many dimensions, and thus equally many experts of different fields would be needed to handle it all. Alicia most certainly wouldn't know. Like I already said, what she told to the king is nothing more or nothing less than what you read in the chapter. Let's
<somehow> make a province of another nation to rebel,
<somehow> keeping our efforts invisible, and then
<somehow> make sure the newly established independent country is very grateful for our help and willing to pay back in exclusive trade deals. Anyone can utter such a line, even an elementary schooler could just repeat such a line from some book they read, but the real issue is what's behind those
somehows. Like I said^2, it's a measure of attitude, nothing else. Of course education can and will massively affect a person's attitude. Impossibilities become possibilities the more you know, although the same is also true for the opposite.
The king wanted to see how the (in)famous girl would react to such a question, whether she would give an answer that makes sense, and what sort of an answer it is, inherently. If it had been some holier than thou answer about simply redistributing wealth between social classes, the king would have judged Alicia much more immature. However, she gave an answer that fits the ways of an absolute monarchy, won't cause internal strife, and in general is fitting for uncaring realpolitik, that is, fitting for a ruler.