What does 1 Kings 2:16 mean?

Adonijah has come to see Solomon's mother, Bathsheba, to formally present a request. For the second time, he has gotten her to agree to hear what he has to say. It's possible that both are playing in a dangerous game of politics and manipulation.

Bathsheba knows how dangerous Adonijah is. Despite assurances that he accepts God's will for Solomon to be king (1 Kings 2:15), Bathsheba knows that if his coronation had succeeded, he almost certainly would have murdered her and Solomon (1 Kings 1:21). He has outright stated that "the kingdom was mine, and that all Israel fully expected me to reign" (1 Kings 2:15), even trying to pull her into that worldview by starting, "You know that…"

The word "speak" is ambiguous. Bathsheba may be naively agreeing to do what he asks, which she will. Or she may be leading Adonijah to say the words that will ensure his demise, which he does. He does most of the talking. She merely encourages him to continue and then agrees to ask Solomon to show him favor.

When Nathan enlisted Bathsheba's help to stop Adonijah's self-coronation and ensure that Solomon became king, he instead told her exactly what to say. It may be that Bathsheba has learned the power of words and the power of letting other people use their words. She needs Adonijah to talk, and he does. She may be following the spirit of the English proverb about "giving a man enough rope to hang himself."