The author here is just throwing a bunch of information about stars at us, so we should start by figuring out exactly what that information is. We're talking about stars, but more specifically about brown dwarf stars. The stimulus gives us various facts about brown dwarf stars: (1) they're too cool to burn hydrogen; (2) they look similar to red dwarf stars; (3) they contain lithium when first formed—because all stars do. Then we learn something about a subset of brown dwarf stars, specifically the coolest brown dwarfs: they have all the properties we've already identified, but they also are the only stars too cool to burn lithium.

From all this, the author concludes that any star lacking lithium cannot be one of the coolest brown dwarfs. We know that all stars contain lithium when they first form, but recall that all stars except the coolest brown dwarfs are hot enough to destroy lithium completely. So the author's reasoning is that if a star is hot enough to have burned away all its lithium, it can't possibly be one of the coolest brown dwarfs.

This might seem like a solid argument now that we've broken it down, but there has to be a gap somewhere to give rise to a necessary assumption. However, the author directly states that the coolest brown dwarfs can't destroy lithium, so that can't be it. As with many Necessary Assumption questions, it might be hard to predict the answer here, so if nothing jumps out straight away a good strategy is to go straight to the answer choices and see what they offer us. We just need to keep in mind that the correct answer must be truly necessary to the argument. If we take the correct answer and tell the argument “you’re not allowed to have this,” the argument will completely fail.

To check whether each answer choice is necessary if it's not immediately clear, we can use one of our tried and true approaches: the "must be true" test or the negation test. Either way, what we're testing that the argument truly requires that assumption.