Free from cares (αμεριμνους). Old compound adjective (α privative and μεριμνα, anxiety). In N.T. only here and Matthew 28:14 which see.

The things of the Lord (τα του Κυριου). The ideal state (so as to the widow and the virgin in verse 1. Corinthians 7:33), but even the unmarried do let the cares of the world choke the word (Mark 4:19).

How he may please the Lord (πως αρεση τω Κυριω). Deliberative subjunctive with πως retained in an indirect question. Dative case of Κυριω. Same construction in verse 1. Corinthians 7:33 with πως αρεση τη γυναικ (his wife) and in 1. Corinthians 7:34 πως αρεση τω ανδρ (her husband).