Why was Annie carried down from the room in a ladder?
In her first day with Helen, Annie is trying to teach her how to "hand speak" she teaches her how to say doll and cake. Helen, a naughty child, throws her doll at Annie, runs and locks the door, so that Annie is locked in. The only way to get her out was for her to be rescued with the ladder.
When Annie was teaching Helen "hand-spelling", writing "doll and cake" on her hand to get each of them as a reward for completing the task, Helen outsmarted and outwitted her by throwing the doll at Annie's face, which hit her and Helen rushed out towards the door, locking Annie inside alone. Annie was unable to find the key to the door, so it was an humiliating experience for her to get "rescued" and safe from the confines of the house by a ladder, which was brought to her window. So, she had to lower her head down in embarrassment and climb down from the room window through the ladder to safety.