Philippians 4:6-9 Be anxious for nothing, but in everything by prayer and supplication, with thanksgiving, let your requests be made known to God; 7 and the peace of God, which surpasses all understanding, will guard your hearts and minds through Christ Jesus. 8 Finally, brethren, whatever things are true, whatever things are noble, whatever things are just, whatever things are pure, whatever things are lovely, whatever things are of good report, if there is any virtue and if there is anything praiseworthy—meditate on these things. 9 The things which you learned and received and heard and saw in me, these do, and the God of peace will be with you.
Here are notes on these verses from Nelson's New Illustrated Bible Commentary:
Philippians 4:6 Paul exhorts the Philippians to pray about their circumstances instead of worrying over them. be anxious for nothing: Although the same word in Php_2:20 describes Timothy's concern for the Philippians, here Paul uses the word to refer to worry. He prohibits the Philippians from worrying about their own problems. Instead they are to commit their problems to God in prayer, trusting that He will provide deliverance.
Philippians 4:7 will guard: Paul's choice of a military term implies that the mind is in a battle zone and needs to be “protected by a military guard.” Since the purpose of such a guard in a wartime situation is either to prevent a hostile invasion or to keep the inhabitants of a besieged city from escaping, the peace of God operates in the same way: to protect the mind from external corrupting influences and to keep the mind focused on God's truth.
Philippians 4:8 noble: This term describes that which is of honorable character. pure: This word is closely associated with the Greek word for holy and thus means “sacred” or “immaculate.” meditate on: Paul commands the Philippians “to deliberate,” “to evaluate,” “to compute over and over” what is good and pure. In this way, Christians can renew their minds so that they will not conform to the evil habits of this world (Rom_12:2).
Philippians 4:9 learned: This verb conveys not only the concept of “increasing in intellectual knowledge” but also the idea of “learning by habitual practice.” In some areas of their Christian development the Philippians had been excellent disciples of Paul, practicing what he had taught. received: This verb (Gk. paralambano) literally means “to take alongside oneself.” It indicates a reception without rejection or disobedience. do: The Philippians are to “put into practice” or “undertake to do” all they had gained from Paul. God of peace: As the Philippians do all that Paul commands, they will realize the presence of God, who is characterized by peace and who is the only source of true peace.
I hope you have found this helpful.