It says in Galatians 2:15-16: "We who are Jews by birth and not 'Gentile sinners' know that a man is not justified by observing the law, but by faith in Jesus Christ. So we, too, have put our faith in Christ Jesus that we may be justified by faith in Christ and not by observing the law, because by observing the law no-one will be justified."
Prior to these verses, Paul has been writing about how he had opposed Peter. The reason for the opposition and correction of Peter was down to the way he was behaving around the Gentiles. According to Paul, he was acting in a hypocritical way, withdrawing from the Gentiles, and towards the circumcision group, who were equally joining Peter in his hypocrisy. And so when we get to verses 15-16, Paul wants to remind Peter, and the readers of the letter (including us today!) that we are justified before God by the work of Jesus, not by keeping the law. Or, in our case, we aren't justified by any of our own works! There is nothing we can do to work our way towards our salvation! We are justified by faith in Jesus, and by faith in Jesus ALONE!
Paul knew that even a strictly observant Jew such as he was (just have a read of Philippians 2:4-5!) could never be considered right before God by what he had done under the law. He wants to really point it out that everyone is justified by their faith in Jesus.
And Paul in his language is very strong in his emphasis. He really wants to make it clear to those he was speaking to, to those he was writing to, and to us today, "by the works of the law no flesh shall be justified." NO FLESH! Not Gentile, not Jew, not anyone will be considered right before God by their works!
As we see later on in the letter, in Galatians 5:6, "The ONLY THING that counts is faith expressing itself through love!"
And so let me finish by asking... have we grasped that we are saved by grace through faith in Jesus? Or are we trying to attain to our salvation through good works? Because Paul spells it out clearly...The only thing that counts is our faith!