Final answer:
A solar system in which a gas giant twice the size of Jupiter orbited its star in the opposite direction to the rest of the planets would be the most challenging discovery for the nebular hypothesis, as it assumes planets in a system should all orbit in the same direction.
Step-by-step explanation:
The nebular hypothesis, which describes the formation of our solar system, suggests that planets formed from a rotating disk of dust and gas around the Sun. Given the options provided, the discovery that would challenge the nebular model the most is (b) a solar system in which a gas giant twice the size of Jupiter orbited the star in the opposite direction to the rest of the planets in that system. This would be particularly difficult to explain with the nebular model because it assumes that all planets form from the same rotating disk of material and thus should move in the same direction.
In comparison, finding a planet half the size of Neptune or dozens of dwarf planets would not contradict the nebular hypothesis as such objects are consistent with current theories of planetary formation. Similarly, a terrestrial planet between gas giants and retrograde moons like Triton can be explained by processes such as planet migration or capture from the Kuiper belt. Thus, although they are intriguing, these discoveries do not present the same level of challenge as a gas giant with a retrograde orbit.