This is the teaching of Our Lord who said μὴ (not) μεριμνᾶτε (be anxious), literally, “(do) not be anxious.”
μὴ μεριμνᾶτε/do not be anxious or carried away about what your life in general (Matthew 6:25): what you shall eat or drink or (have to) wear (Matthew 6:31; Luke 12:22)—to do so is to not trust in God who provides; the heathens are such as seek to be prepared and always one step ahead in their material belongings and welfare (Matthew 6:32; Matthew 6:26).
And μὴ μεριμνᾶτε/do not panic about confrontation with the enemy because God will beat out the path for you in that moment (Matthew 10:19).
Thus, “Be not anxious, but in everything by prayer and supplication with thanksgiving let your requests be made known to God” means Do not be overcome with worldy cares, but trust in the provident God who provides for all, because He is faithful and willing to provide (Matthew 7:7; 21:22).