I am still trying to understand the proposed English sentence. It sounds very unfamiliar to me and I associate "How are you?", "How am I?"; ... My intuition warns and rewrites that sentence to "How do i dare to reply to Katerina?"
Google proposed only rare examples for this composition, all lyrics (like the song "How am i to know"). I did not find similar things in any of my favourite dictionaries. Is it a kind of slang or idiom as my intro suggests?
Word by word to German: "Wie habe ich Katerina zu antworten?" means "How do i have to reply to Katerina?" (was not accepted, when using "answer" instead of "reply") which is stricter than "How am i supposed to reply to Katerina?"