The correct answer is (c) by.
Preposition Rule:
"Live by" = to survive or support oneself through a particular method, principle, or means.
→ "He lives by honest means" = সে সৎ উপায়ে জীবিকা নির্বাহ করে।
Related usage:
— live by one's principles (নিজের নীতি মেনে জীবন যাপন)
— live by the sword (তরবারির জোরে বাঁচা)
— He earns his living by teaching.
✗ "live on" = to survive on a particular food or amount of money (He lives on rice / He lives on a small income).
✗ "live with" = to reside with someone.
✗ "live for" = to dedicate one's life to something.
Source: Oxford Advanced Learner's Dictionary; Longman Dictionary of Contemporary English.