를 먹고

eat … and

→ 를
phrase Common #5,301
eat … and 를 marks the object of 먹다, “to eat.” 먹고 connects it to what follows, often meaning “eat … and” or “after eating ….”
KO: 바나나를 먹고 산책했어요.
EN: I ate a banana and went for a walk.

뭐를 먹고 계세요?

What are you eating?

— 담뽀뽀 (1985)