God has promised that you will experience his perfect peace when your eyes are fixed on him. The peace that God gives is not like peace from the world (John 14:27). His peace secures your body, mind and emotions. It is an experiential peace, not a mental gimmick.
In order to receive this real peace, we are given something to do. We are called to have a "steadfast mind." What is this? It is literally to have a mind that is leaning, resting or bracing itself on God. This is an active process. The way of peace is not clearing one's mind of all thoughts and emotions. That is Buddhism. And that leads to destruction. God's pathway of peace for us involves bracing or leaning one's mind against who we know God to be. We actively recall God's character to our minds. We speak out the truth of God's power and care over our lives.
This might sound like a difficult task - to lean one's mind against God. But, our Father never gives us an impossible task. We play a crucial part in the fulfilling of God's promise. He wants to work with us in experiencing his peace. We can practice leaning into his character. In this way, we can actually begin living in his perfect peace, as opposed to knowing this peace in sporadic moments through life.