“How could you buy them without consulting with me?”
You and your husband were thinking of going on an overseas vacation. Today he bought plane tickets for both of you. You're upset because he didn't call you before he bought them, and you don't like some of the flight details. Annoyed, this what you ask him.
How could you buy them without consulting with me?
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How could you (do something)
"How could you...?" means "I can't believe you did that" and "You shouldn't have done that":
How could you say that? I thought you loved me?
How could you lose a three thousand dollar check? What is wrong with you?
When the wife asks her husband "How could you buy them...?" she doesn't really want to know how. She wants to know why he bought the tickets without asking her first. She's also angry about him doing that.
them
"Them" in this example means airplane tickets.
(do something) without consulting with (someone)
To "consult with" someone means to talk with them in order to get help making a decision:
Consult with a doctor if you think you might have some kind of health issue.
I need to consult with my manager before I can agree to that price.
When someone is supposed to discuss an issue with someone, but doesn't, use the phrase "___ without consulting with ___":
In the future, don't make any purchases without consulting with me please.
You can also say "without consulting (someone)":
How could you buy them without consulting me?