Justified by faith in Christ, Galatians 2:16

Galatians 2:11  Now when Peter had come to Antioch, I withstood him to his face, because he was to be blamed; 
12  for before certain men came from James, he would eat with the Gentiles; but when they came, he withdrew and separated himself, fearing those who were of the circumcision.
 13  And the rest of the Jews also played the hypocrite with him, so that even Barnabas was carried away with their hypocrisy. 
14  But when I saw that they were not straightforward about the truth of the gospel, I said to Peter before [them] all…

Paul confronts Peter because his actions send a message that we are justified, declared righteous, by the works of the Law and not by faith in Christ. 
Certain Jews believed one must keep the Law to be saved, and that included non-association with Gentiles. 
Peter would keep company with gentiles, but withdraw from them when certain legalistic Jews appeared.

The Apostle Paul in Galatians 2.16 says: knowing that a man is not justified by the works of the law but by faith in Jesus Christ, even we have believed in Christ Jesus, that we might be justified by faith in Christ and not by the works of the law; for by the works of the law no flesh shall be justified.

This is a good text to set forth that it is through faith in Christ and not the works of the Law by which we are justified--declared righteous before God.  

There is a genitive case issue here that some use to support their King James Only view. The genitive here is translated by most translations as “in Jesus Christ”;  the KJV and Youngs  translate  it as “of Jesus Christ”--which some argue to say it is Jesus’ faith that justifies us.  The genitive speaks of possession, and here it would be a subjective genitive, as in it is Christ’s faith that he had.

But the verse also says that we have believed so the we “might be justified by faith of/in Christ.” So the recipient of this justification does have to believe in something.

The NET Bible translates the genitive as speaking of this faith of Christ as in the faithfulness of Christ--which then could be understood as his obedient sacrifice by which we are justified.  That could work...but I believe it is best to go with what most translators understand the genitive  to mean, and that is that it is faith in Christ as the object of faith.

Justification is not "by" works but "by" faith.

In Galatians 2:16, the word "by" in all but the second instance is the Greek preposition "ek" which means "out of" or "from" and signifies source. The second instance is the Greek preposition "dia" which means "through" or "by means of" signifying instrumentality as in Ephesians 2.8-9.

Paul uses contrasts here. We are justified not out of works, but out of faith. 

The Greek preposition dia is used in similar fashion as Ek, to show the condition.  Justification is conditional, but the condition must be rightly understood.  Works of the Law should be understood as our own righteousness as the grounds of acceptance—but Paul says no flesh will be justified by it; for if that were possible or the way, Christ died in vain, Galatians 2:21.  

It is by faith in Christ for salvation, by which we are declared righteous.  So the difference is our own righteousness verses the righteousness given.