(E) says, "Although flawed in certain respects, Williams’ conclusions regarding the economic condition of British slave colonies early in the nineteenth century have been largely vindicated."
The problem with (E) is that it's false. Wek now that economics played a role because of Eltis; however, Williams was not correct in the reasons as to why that ended up being the case (look at lines 60-61). If someone gets the "why?" part wrong, there's no way that they can be largely correct, so this is why (E) can be eliminated.
(B) says, "Although both Drescher and Eltis have questioned Williams’ analysis of the motivation behind Britain’s abolition of slavery, there is support for part of Williams’ conclusion."
Lines 54-58 are crucial for being able to spot (B) as the correct answer, as it's where the main point of the passage is revealed. "Eltis thus concludes that, while Williams may well have underestimated the economic viability of the British colonies employing forced labor in the early 1800s, his insight into the economic motives for abolition was partly accurate" is the main idea of this passage. In the correct answer choice, we want something that discusses the critiques of Williams' work while still maintaining that it's at least partially supported. (B) gives us nicely, so it's the correct answer choice.
Does this make sense? Let us know if you have any other questions!