The verse begins with a strong contrast: about nothing worry, but in everything by prayer and supplication . . .
Meyer identifies μηδὲν as the accusatival object of μεριμνᾶτε and it seems evident that Paul emphatically prefixes μηδὲν, thus drawing attention to "nothing." ἐν παντὶ is also meant to be a contrast with the opening words (Meyer). Furthermore, maybe we should understand ἐν παντὶ to signify "in every case or affair" (Meyer). ESV also renders ἐν παντὶ τῇ προσευχῇ "in everything by prayer," NET has "in every situation, through prayer" and HCSB renders the words, "in everything, through prayer . . ."
With the phrase, ἐν παντὶ, παντὶ is a substantival adjective and the prepositional object of ἐν.
Should we make a sharp distinction between τῇ προσευχῇ καὶ τῇ δεήσει?
According to John Eadie:
The form which the presentation of such requests was to assume was τῇ προσευχῇ καὶ τῇ δεήσει—“by prayer and supplication.” The datives express the manner or means, for the one involves the other, by which the action enjoined in γνωριζέσθω was to be performed. Bernhardy, p. 100. The two nouns are not synonymous, and mean something more than Storr's sociis precibus. See under Ephesians 6:18 for the peculiar distinction. The repetition of the article gives each of the nouns a special independence. Winer, § 19, 5, (a). By the use of the first noun they are bidden tell their wants to God in religious feeling and form; and by the second they are counselled to make them known in earnest and direct petition, in every case as the circumstances might require.
Along with supplications (earnest beseeching), add μετὰ εὐχαριστίας.
Gerald F. Hawthorne construes τὰ αἰτήματα ὑμῶν γνωριζέσθω πρὸς τὸν θεόν to signify that prayer is a uniquely intimate way of approaching God: "Let God know what is troubling you" (Word Commentary on Philippians, page 183. Volume 43, 1983 edition).
From the Expositor's Greek Testament:
αἴτημα is found three times in N.T. It emphasises the object asked for (see an important discussion by Ezra Abbot in N. Amer. Review, 1872, p. 171 ff.). “Prayer is a wish referred to God, and the possibility of such reference, save in matters of mere indifference, is the test of the purity of the wish” (Green, Two Sermons, p. 44).—πρὸς τ. Θεόν. “In the presence of God.” A delicate and suggestive way of hinting that God’s presence is always there, that it is the atmosphere surrounding them. Anxious foreboding is out of place in a Father’s presence. Requests are always in place with Him. With this phrase Cf. Romans 16:26.
καὶ ἡ εἰρήνη τοῦ θεοῦ: The ICC Commentary says καὶ here is "consecutive." Hence, translate "and so."
There is scholarly debate concerning the nature of divine peace. Is it internal or external? Furthermore, Paul probably has the Hebrew shalom in mind when he uses the noun phrase ἡ εἰρήνη. τοῦ θεοῦ is possibly a subjective genitive.
ἡ ὑπερέχουσα πάντα νοῦν (vs. 7)
Eadie offers this explanation: "The participle here [ἡ ὑπερέχουσα] governs the accusative, and not, as is common with verbs of its class, the genitive, Kühner, § 539; or Jelf, § 504, Obser. 2."