Which work of Francis Bacon explains the new logic or inductive method of reasoning?

The correct option is Novum Organum.

Francis Bacon was a seminal English philosopher and statesman who is widely regarded as the father of modern empiricism and the scientific method. His work aimed at reforming the process of scientific inquiry.
The title Novum Organum translates from Latin to "New Instrument" or "New Tool". This title was a direct reference to Aristotle's work on logic, known as the Organon ("Instrument"). By naming his work Novum Organum, Bacon proposed a new system of logic to replace the traditional Aristotelian syllogism and deductive reasoning.

Bacon's new system is built upon the inductive method of reasoning. Unlike deductive reasoning, which starts with general premises to reach a specific conclusion, Bacon's inductive reasoning begins with systematic, empirical observations of nature. By gathering facts, performing experiments, and carefully analyzing data, inquiries progress from specific observations to broader, general scientific laws.
Therefore, Novum Organum is the specific work of Francis Bacon that details and advocates for this new inductive method, paving the way for modern scientific investigation.