Great question. Let's first take a look at the definition of the word "concede."
1. admit that something is true or valid after first denying or resisting it.
2. surrender or yield (something that one possesses).
Now, let's take a look at the stimulus. The argument is saying that adolescents should also be able to vote. The rationale is that adolescents and adults aren't the same, but adults can't represent the interests of adolescents because they're different. And since adults can't represent the interests of adolescents, then the only way to allow adolescents to be represented is by allowing them to vote.
The main point of the argument is that adolescents should be able to vote just like adults do. The support is that adults and adolescents are different, and the argument discusses that adults cannot represent the interests of adolescents since they're different. The entire stimulus after the first sentence is used as support for the overall conclusion (which is the first sentence).
The question says, "The statement that adolescents and adults are not the same plays which one of the following roles in the argument?"
We're looking for the role this plays. We know it's part of the premise, so let's look at the answer choices.
(E) says, "It concedes a point that is then used to support the conclusion."
This is great. "Admittedly," which is the word that the second sentence starts with, signifies that what follows is a concession (giving up a point). Then, throughout the premises, the same point that was given up (that adults and adolescents are different), is used as support for the overall conclusion. This is a great answer, and it's exactly what we're looking for.
It sounds like you may not have had a complete understanding of what the word "concedes" means. Be sure to review the definition, which is provided above, as this word will undoubtedly show up on subsequent LSAT questions.
Does this help? Let us know if you have any more questions!