Step 1: Oxidising agent definition.
An oxidising agent is a substance that gains electrons and, in the process, causes another substance to lose electrons. In this reaction, oxygen \( O_2(g) \) is reduced to \( H_2O(l) \), which means that it accepts electrons. Hence, oxygen is the oxidising agent.
Step 2: Analyzing the options.
(A) \( CH_4(g) \): This is incorrect. Methane is being oxidised, not reduced.
(B) \( O_2(g) \): This is the correct answer because oxygen is gaining electrons and is the oxidising agent.
(C) \( CO_2(g) \): This is incorrect, as \( CO_2(g) \) is the product of oxidation.
(D) \( H_2O(l) \): This is incorrect, as water is formed during the reaction and is not involved in oxidation.
Step 3: Conclusion.
The correct answer is (B) \( O_2(g) \).