What does Romans 2:6 mean?

In the previous verses, Paul has harshly condemned any moral or religious persons guilty of judging others for their sinfulness (Romans 2:1–3). Paul has hinted at the truth he will spell out in the following chapter: We are all sinners (Romans 3:23). None of us should presume that God will not express His wrath on us because of our sinfulness.

Now Paul begins to describe the absolute law of who will receive eternal life with God, and who will receive "wrath and fury" (Romans 2:8) from Him, instead. Paul quotes from Psalm 62:12 and Proverbs 24:12 to articulate the universal truth that God will give to each person according to his works. He describes the difference between those who will receive wrath or reward from God in the following verses.

Taken out of context, this is a troubling statement. Paul seems to indicate that God judges all people on the basis of their behavior. However, this is the same idea expressed by Jesus Himself (Matthew 16:27). In terms of reward, this is absolutely true; each person is judged on the basis of their deeds (Romans 14:10–12; 2 Corinthians 5:10). However, as Paul will make clear in this letter, nobody can be saved by their good deeds (Romans 3:23). Our only hope for salvation—for rescue from the penalty of our sin—is grace, through faith in Jesus Christ.