I think the reason why Peter had a hard time understanding Paul is because Paul's arguments are linear. He builds them one step at a time. This is to our advantage because Western culture also builds arguments in linear fashion, step-by-step. So then, if you don't mind, let's work through his argument from top down and see how he is building it.
Beginning with verse 12
12 For all who have sinned without the Law will also perish without the Law, and all who have sinned under the Law will be judged by the Law;
The statement above is like his thesis statement for this section. He simply asserts that sinners perish. Whether the individual is a Gentile without the Law or a Jew under the law, either way sinners perish. In other words, with regard to the final judgment, having the Mosaic Law does not give the Jews an advantage. He will argue later that in-so-far as knowing God's will for mankind, the Jews have an advantage in that they were given the oracles of God. But with regard to salvation, they are on the same level playing field as the Gentiles, so to speak.
13 for it is not the hearers of the Law who are just before God, but the doers of the Law will be justified.
Here Paul begins to argue the case. He must answer why is it that sinners perish. In this paragraph, Paul will argue his case for why Gentile sinners perish. Beginning in verse 17 and continuing for two paragraphs, he will argue why it is that Jewish sinners perish. His readers and perhaps his objectors would likely agree that the Law condemns us, not for things we hear, but for things we do or fail to do. If anyone is looking for justification, they will be justified by the law if they actually do the law.
At this point, someone might raise an objection. With regard to the Gentiles, they neither hear the law or obey the law. How can a Gentile find justification in a law they don't know? In other words, is it fair for God to sentence someone to perish if he hasn't had a chance to obey divine law in the first place?
14 For when Gentiles who do not have the Law do instinctively the things of the Law, these, not having the Law, are a law to themselves,
Paul grants that the Gentiles are unaware of God's law. However, he argues that although the Gentiles don't have access to the law of Moses, it isn't as if they are unaware of divine law. He says, the Gentiles instinctively do the things of the law. Though the Gentiles don't have access to the oracles of God, they have intuitively figured out a code of behavior based on objective morality.
He says that the Gentiles are "a law to themselves" and I think he is using "nomos" to mean something like covenant, agreement, or compact. Gentile jurisprudence relies on mutual agreement, whereby men agree to live by a set of laws for the mutual benefit of all. So, even though they don't have God's oracles, they have laws concerning behavior based on moral principles of right-and-wrong, fairness, and justice.
15 in that they show the work of the Law written in their hearts, their conscience bearing witness and their thoughts alternately accusing or else defending them,
One might argue that a sinner is a person who transgresses against divine law by committing an immoral act or acts. I believe Paul is attempting to argue that Gentiles are also subject to divine justice because they adjudicate objective morality in their own minds. Divine law is universal because, being made in the image of God, all human beings intuitively know right from wrong. The work of the law, then, is manifest in the conscience of mankind where morality is adjudicated in our thoughts, which either accuse us or defend us.
16 on the day when, according to my gospel, God will judge the secrets of men through Christ Jesus.
On judgment day, then God will judge the thoughts of men, i.e. the secrets of men, through Christ Jesus. Gentile sinners perish because they know right from wrong.
I realize this is a long post, but hopefully the answer to our question is in there somewhere. What do you think?