Free from cares (amerimnous). Old compound adjective (a privative and merimna, anxiety). In N.T. only here and Mat 28:14 which see.
The things of the Lord (ta tou Kuriou). The ideal state (so as to the widow and the virgin in 1Co 7:33), but even the unmarried do let the cares of the world choke the word (Mar 4:19).
How he may please the Lord (pōs aresēi tōi Kuriōi). Deliberative subjunctive with pōs retained in an indirect question. Dative case of Kuriōi. Same construction in 1Co 7:33 with pōs aresēi tēi gunaiki (his wife) and in 1Co 7:34 pōs aresēi tōi andri (her husband).