Final answer:
Science cannot predict the exact date when the sun will burn out, as it goes beyond empirical evidence and observable phenomena that science relies on.
Step-by-step explanation:
The question that science cannot answer from the list provided is: What will be the date when the sun burns out? This question involves making predictions that go beyond empirical evidence and cannot be tested or observed directly. Scientific methods rely on observation, experimentation, and repeatability to provide empirical evidence and formulate theories. Questions like the phases of the moon, how green plants make food, and the time it takes for the Earth to orbit the Sun can be answered through scientific investigation and are based on observable phenomena. On the other hand, predicting the exact date of the sun's demise falls into the realm of speculation since it deals with an event far in the future, for which no direct observations can be made at present.