“What about…?” and “How about…?” are very similar, but there is a slight difference.
Use “How about?” to suggest an action and to “open” possibilities:
“I’ve got the day off from work tomorrow. What should we do?”
“How about spending the day in the city?”
“Nah. I don’t really feel like traveling.”
“How about we clean the house?”
“No way. I want to do something fun.”
“OK. How about doing some shopping and then seeing a movie?”
“Hmm… that sounds good!”
In this conversation, “How about…?” is use to suggest various possibilities of actions.
“How about…” can be followed by the -ing form of the verb OR by a pronoun and infinitive (“How about we clean…”)
Use “What about?” to mention an objection or a potential problem:
“Let’s spend the weekend in the city!”
“But what about my guitar lesson on Saturday?”
“That’s no problem, just talk with the teacher and reschedule it.”
“And what about the English test on Monday? I haven’t studied yet.”
“You can study on Sunday night when we get back.”
In this conversation, “What about…” is used to express a negative point or a potential problem with the plan or idea. After “What about…” there is a noun (“my guitar lesson” and “the English test”)
“How about you?” and “What about you?” are both correct!
“How have you been?”
“Good – a little busy with school. How about you?”
“Where do you work?”
“At the local university. What about you?”
In this case, How about you? and What about you? are asking the same question back to the other person.