Well, here's a question for you. What did I come here to do?
"はて、あなたに問題です 私は今日何しに来たでしょう?" は英語で
Well, here's a question for you. What did I come here to do (today)? といえます。
はて = well; then
あなたに問題です = here is a question for you; this is a question for you
私は今日何しに来たでしょう = What did I come here to do today?
I have something I'd like to ask you. Why do you think I came here today?
I have a question for you. What do you think I'm doing here today?
ーI have something I'd like to ask you. Why do you think I came here today?
「あなたに質問です。私は今日なぜここに来たでしょうか?」
Why do you think ...? 「なぜだと思いますか?」を使って聞くことができます。
ーI have a question for you. What do you think I'm doing here today?
「あなたに質問です。私は今日ここで何をしていると思いますか?」
What do you think ...? 「あなたはどう思いますか?」を使っても聞くことができます。
ご参考まで!