And - The inseparable consequence of thus laying everything before God in “prayer with thanksgiving.”
peace - the dispeller of “anxious care” (Phi 4:6).
of God - coming from God, and resting in God (Joh 14:27; Joh 16:33; Col 3:15).
passeth - surpasseth, or exceedeth, all man’s notional powers of understanding its full blessedness (1Co 2:9, 1Co 2:10; Eph 3:20; compare Pro 3:17).
shall keep - rather, “shall guard”; shall keep as a well-garrisoned stronghold (Isa 26:1, Isa 26:3). The same Greek verb is used in 1Pe 1:5. There shall be peace secure within, whatever outward troubles may besiege.
hearts and minds - rather, “hearts (the seat of the thoughts) and thoughts” or purposes.
through - rather as Greek, “in Christ Jesus.” It is in Christ that we are “kept” or “guarded” secure.