The answer 88.24% is correct. This is a conditional probability question, which can be solved using Bayes Theorem:
The probability that she knew the material given that she got the answer right = P(she knows | she got it right) = P(she knows AND got it right)/P(She got it right) = 0.6/0.68 = 0.8824.
Another way to think it thorugh is like this: there are 68 correct answer ouit of 100, and 60 of those are becuase she knew the material, so 60/68 = 0.8824.
Your other approach is incorrect because P(K) does not equal P(C)-P(G) as you've defined them. P(G) should properly be defined as the probability that she guessed given that she got it right, which is 8/68. So then your approach becomes P(K|C) = P(C) - P(G|C) = 1-0.1176 = 0.8824.