Romans 1:32 Although they know God's righteous decree that those who do such things deserve death, they not only continue to do these very things but also approve of those who practice them.

Men do not sin out of ignorance. With full knowledge that what they are doing is wrong, and that the penalty of sin is death, eternal death, they continue to choose sin.It is a great aggravation of sin when it is committed against knowledge (James 4:17), especially against the knowledge of the judgment of God.  It argues the heart much hardened, and very resolutely set upon sin.

James 4:17 Anyone, then, who knows the good he ought to do and doesn't do it, sins. 

Romans 1:32 Although they know God's righteous decree that those who do such things deserve death, they not only continue to do these very things but also approve of those who practice them.

They do not only commit sin, but they defend and justify it, and encourage others to do the like. Our own sins are much aggravated by our concurrence with, and complacency in, the sins of others.  Gay Marriage comes to mind.

Now lay all this together, and then say whether the Gentile world, lying under so much guilt and corruption, could be justified before God by any works of their own.

Why do people continue sinning if they know that "those who do such things deserve death"?

What do the following passages have to say about that?  

Matthew 5:21-22 21"You have heard that it was said to the people long ago, 'Do not murder, and anyone who murders will be subject to judgment.' 22But I tell you that anyone who is angry with his brotherwill be subject to judgment. Again, anyone who says to his brother, 'Raca,' is answerable to the Sanhedrin. But anyone who says, 'You fool!' will be in danger of the fire of hell. 

Matthew 5:27-28 27"You have heard that it was said, 'Do not commit adultery.' 28But I tell you that anyone who looks at a woman lustfully has already committed adultery with her in his heart. 

Romans 3:9-12  9What shall we conclude then? Are we any better?  Not at all! We have already made the charge that Jews and Gentiles alike are all under sin. 10As it is written: "There is no one righteous, not even one; 11there is no one who understands, no one who seeks God.
 12All have turned away, they have together become worthless; there is no one who does good, not even one." 

James 2:10-11 10For whoever keeps the whole law and yet stumbles at just one point is guilty of breaking all of it. 11For he who said, "Do not commit adultery," also said, "Do not murder." If you do not commit adultery but do commit murder, you have become a lawbreaker.     
 

As an illustration of how total mankind’s rebellion against God is, compare the description of human behavior found in this week’s passages with the Ten Commandments (Deuteronomy 5:6-21).