The words of Jesus to which you refer are found in what we call the Sermon on the Mount: "But I tell you, Do not resist an evil person. If someone strikes you on the right cheek, turn to him the other also" (Matthew 5:39).
It's important to remember that Jesus was speaking these words to His disciples, telling them how they were to live in a world that might be hostile to them. He wasn't telling nations how they ought to deal with each other, or giving us a general rule for human society. In fact, the Bible says governments should uphold what is right, and when evil men seek to gain the upper hand they must be restrained and punished (see Romans 13:4).
What did Jesus mean when He urged His followers to turn the other cheek? Simply this: He was telling them to take the path of love instead of hate. Anger and hatred lead to revenge and conflict—but Christ calls us to love others, even our enemies. Just a few verses later, He said, "I tell you: Love your enemies and pray for those who persecute you" (Matthew 5:44).
Is this possible? Yes—when we commit our lives to Christ and allow His Spirit to control us. This is the kind of love Jesus had for us, when He died for us on the cross. Have you opened your heart to Him? If not, make your commitment to Him today, and then ask Him to begin filling your heart with His love.