The phrase 'to be at sixes and sevens' means to be confused or in some kind of uproar. Before Annie taught Helen how to behave, Helen kept the entire house in turmoil with her actions.

Her tantrums caused stress between the mother and father. She would pout, throw things, and physically lash out at those around her. The entire household was focused on keeping her happy and calm, a nearly impossible task. 

Because Helen was the center of this chaotic world, no peace could settle on the house. The family could not have relaxing family dinners around the table; they couldn't go out together in public to any entertaining events. Helen's father couldn't even find peace and quiet to read a newspaper.

When Captain Keller says his house is at sixes and sevens, he is expressing his frustration at the constant turmoil Helen's behaviors cause. He desires a calm, orderly home, and until something is done about Helen's out of control antics, he won't get it.

What does Captain Keller mean by "the house is at sixes and sevens"?

The phrase “at sixes and sevens” means that everything is thrown into confusion because of Helen’s uncontrolled behavior. The phrase comes from a dice game, when everything is bet with a very high risk by rolling either a six or seven.

Helen has been allowed to have the run of the house, as her family believes she cannot be trained because of her disabilities. She takes what food she wants from the plates of others at the dinner table, and is not taught to sit down and eat like the rest of the family. If she is thwarted in anything, she throws a temper tantrum. The entire family must adjust everything they do to make way for Helen. It is for this reason that Captain Keller sends for a teacher from the North, though he is skeptical about how much Helen can be taught. The family cannot long continue in the midst of such chaos. The only other option is to send Helen to an institution for the mentally ill.