Based on the level of respect or formality, you can say "Can you do me a favor?" in Korean in 3 ways:

• Informal: neo-ege butak jom haedo doilgga? (너에게 부탁 좀 해도 될까?), neo-ege butak jom haedo doini? (네게 부탁 좀 해도 되니?)
• Formal: dangsin-ege butak jom haedo doilggayo? (댱신에게 부탁 좀 해도 될까요?), dangsin-ege butak jom haedo doigetseupnigga? (당신에게 부탁 좀 해도 되겠습니까?)
• Very Formal: dansin-ggeseo-neun butak jom deuryeodo doigetseupnigga? (당신께 부탁 좀 드려도 되겠습니까?)

- can do: hal su ittda (할 수 있다)
- you (subjective): neo-ege (너에게), dangsin-ege (댱신에게), dansin-gge (당신께)
- to do a favour: butak jom hada (부탁하다)
- me: na-reul (나를), jeo-reul (저를) - omitted here


Please refer to How to pronounce Korean Alphabet for the English pronunciation in this answer.