How can I experience the "peace that passes understanding" (Philippians 4:7)?
You know that peace, according to Paul in Philippians 4, when you pray, bringing your anxiety to God: "Have no anxiety at all, but in everything, by prayer and petition, with thanksgiving, make your requests known to God. Then the peace of God that surpasses all understanding will guard your hearts and minds in Christ Jesus" (Philippians 4:6-7).
The other key, besides prayer, is to get your focus right. What things should you be focusing on? Paul writes: "Finally, brothers, whatever is true, whatever is honorable, whatever is just, whatever is pure, whatever is lovely, whatever is gracious, if there is any excellence and if there is anything worthy of praise, think about these things. Keep on doing what you have learned and received and heard and seen in me. Then the God of peace will be with you" (Philippians 4:8-9).
Try to develop the habit of reading scriptures in context. Reading single verses will not go very far in explaining the will of God. Yet most Christians read only isolated verses, and never develop the habit of understanding a verse in light of the whole message (in this case, Paul's letter to the Philippians). The answer to your question was right under your nose, but because you were reading the text in isolate sections, you did not get a proper sense of the whole.