Hampshire's assertions, far from showing that we can (i) _______ the ancient puzzles about objectivity, reveal the issue to be even more (ii) _______ than we had thought.

Once you read it, you will understand the key is deciphering blank (i). From the way the sentence is structured, we get to know the nature of the word to be negative - in lines reject, ignore. Best suitable option is "dismiss"

Now coming to blank (ii), if you simply look at the options - all would seem to fit. This is one of the typical trap questions, where you need to formulate a guess based on:
1. when read - you will understand it should be opposite in nature to blank (i) due to the keywords "far from" - hence deciphering blank(i) is critical
2. other words like "ancient" and "objectivity" give the needed context

Lets look at the options now:
elusive - it seems as though "dismiss" and "elusive" seem to run in similar directions - hence not what you need
relevant - sounds positive and somewhat opposite to "dismiss", then bring in words like "ancient" it would seem to fit better
unconventional - doesnt fit here, no sufficient keyword to support it

What is the clue or evidence for dismiss?

Hampshire's assertions, far from showing that we can (i) _______ the ancient puzzles about objectivity, reveal the issue to be even more (ii) _______ than we had thought.

Far from means that we cannot dismiss AND also tells us that the issue is relevant

What does it show us ?? that we cannot dismiss it or overlook ?? why ?? because it is relevant more than we thought

Hope this helps