verbs with two direct objects
Solution 1:
"Let me ask you a question" is probably the most common way to say this. This is basically the same construction as "I ask you a question." But you is not a direct object. When we say this, it implies that we are saying something more like, "Let me ask [to you] a question." Because the question is being addressed to a person, this would seem to be the most correct usage, but in English, this is very unnatural and awkward. "Let me ask a question [of you]." is acceptable, even though what we want of them is an answer, not a question. But this still is a bit odd. "Let me ask you a question" or "Let me ask you something" is far more common.