Milo changes from the beggining of act ii to the end of act ii of the phantom tollbooth. what is the biggest change in him

At the start of The Phantom Tollbooth, Milo is just a boy, a bored boy who's not satisfied by anything. When he's introduced to us at the beginning of the book, it seems like his most prominent characteristic is, in fact, being bored:

When he was in school he longed to be out, and when he was out he longed to be in. On the way he thought about coming home, and coming home he thought about going. Wherever he was he wished he were somewhere else, and when he got there he wondered why he'd bothered. Nothing really interested him – least of all the things that should have. (1.2)

It's like the grass is always greener on the other side for him: he's always dissatisfied. But Milo's not a bad kid: he just doesn't know any better than to be bored. Once he gets going, we – and he – discover that he's got a great sense of adventure.

Practically the first thing he does is the Lands Beyond is conquer his boredom, by seeing what happens to others when they're bored (the Lethargarians in the Doldrums). Milo very quickly realizes the danger of doing nothing, and he sees the effects of this in the Lethargarians, even though he couldn't see it in himself. Lesson learned. But wait, there's more

he is suggesting that this widow is a strong woman, who is giving constructive criticism and she has enough to worry about, and she takes care of him, so he does not take it to heart.