This is a must be true question, so we're looking for the answer choice that's something that has to be true based on the information in the stimulus.
(A) says, "Some of the medieval manuscripts whose authenticity is suspect are frequently consulted by researchers."
From the stimulus, we know that 1) most medieval manuscripts of cultural significance will be restored, 2) some manuscripts with suspect authenticity will be restored, 3) if a manuscript is restored, its safety can be ensured, and 4) if a manuscript isn't frequently consulted, it won't be restored
The second and fourth premises from the stimulus combine to give us this answer choice. Take the contrapositive of the fourth premise and connect it to the second premise
manuscripts with suspect authenticity - some - restored - >frequently consulted
This means that some manuscripts with suspect authenticity are frequently consulted, leading us to (A).
(C) says, "All of the medieval manuscripts whose safety can be ensured during the restoration process are frequently consulted by researchers."
The problem with (C) is that the things that it discusses are both on the necessary side of their conditional statements. If we switched "all" with "some," then this statement would be o.k. However, we can't combine the premises from the stimulus to push out (C) as it's written with "all," so this answer choice doesn't work.
Does this make sense? Let us know if you have any more questions!