These are usually some of the toughest questions. When I was doing these I would always go through the answer choices and ask myself: "If this is true, could the author's argument still be valid?" The correct answer is always the one that undermines something fundamental about the authors argument. So, if answer choice is correct, the author can't possibly be correct. The problem is it's really easy to get side tracked by the answer choices that would hurt the authors argument but not undermine it.
Here's a simplified example:
Let's say the author argues that people shouldn't be able to vote until their 25 years old because young people don't research anything before they vote.
The question is, which of the following would must undermine the author's argument.
A) A study proves that young people research issues just as much as older people before they vote.
B) A study that proves senior citizens rarely research anything before they vote.
C) When polled, young people are rarely aware of current events
D) A study shows that 26 year olds are just as misinformed about current events as 18 year olds.
Going through the answer choices, only answer A totally undermines the authors argument. If it is true, the justification given for changing the voting age is wrong. Answers B and D might hurt the author's argument but it could still be true. We can eliminate C because it supports the author's argument