6:1 Τὰ τέκνα, ὑπακούετε τοῖς γονεῦσιν ὑμῶν [ἐν κυρίῳ]· τοῦτο γάρ ἐστιν δίκαιον.
Τὰ τέκνα – Vocative, defining the subject of ὑπακούετε. τέκνα may refer to adult progeny.
ὑπακούετε τοῖς γονεῦσιν ὑμῶν [ἐν κυρίῳ] – Present active imperative. The dative case defines the object, which is modified by a genitive of relationship. Whether the adverbial prepositional phrase is original or not remains debated, but the longer text seems to have the better textual support. If it is original, then it is modifying the verb and describing the manner or the referential framework in which these progeny are to obey their parents.
τοῦτο γάρ ἐστιν δίκαιον – An explanatory aside marked by γάρ, which affirms the appropriateness of this obedience in God’s eyes. τοῦτο refers the entire previous command and the subject of the equative clause.
6:2 τίμα τὸν πατέρα σου καὶ τὴν μητέρα, ἥτις ἐστὶν ἐντολὴ πρώτη ἐν ἐπαγγελίᾳ — The quotation is from Ex. 20:12 or Deut. 5:16.
Ex. 20:12 τίμα τὸν πατέρα σου καὶ τὴν μητέρα, ἵνα εὖ σοι γένηται καὶ ἵνα μακροχρόνιος γένῃ ἐπὶ τῆς γῆς τῆς ἀγαθῆς, ἧς κύριος ὁ θεός σου δίδωσίν σοι.
Deut. 5:16 τίμα τὸν πατέρα σου καὶ τὴν μητέρα σου, ὃν τρόπον ἐνετείλατω σοι κύριος ὁ θεός σου, ἵνα εὖ σοι γένηται καὶ ἵνα μακροχρόνιος γένῃ ἐπὶ τῆς γῆς, ἧς κύριος ὁ θεός σου δίδωσίν σοι.
It is impossible to say which text Paul is using.
τίμα τὸν πατέρα σου καὶ τὴν μητέρα — The main verb is a present active imperative, which is modified by a compound direct object. The genitive possessive pronoun indicates relationship and does not need to be repeated (as occurs in Deut, which might suggest Paul was referencing the Exodus version).
ἥτις ἐστὶν ἐντολὴ πρώτη ἐν ἐπαγγελίᾳ — ἥτις is a feminine form of a relative pronoun which can communicate the sense “which is the kind…,” but may just serve a stylistic variation for the usual relative pronoun. The antecedent follows in ἐντολή. This is an equative clause and ἐντολὴ πρώτη functions as a predicate noun. The adverbial prepositional phrase expresses that with reference to which the command is first.
6:3 ἵνα εὖ σοι γένηται καὶ ἔσῃ μακροχρόνιος ἐπὶ τῆς γῆς.
ἵνα εὖ σοι γένηται – This is the second part of the quotation. This is not in the Hebrew text of Exodus, but does occur in the Hebrew text of Deut. It is in the Greek texts of Exodus and Deuteronomy. It is a purpose clause marked by ἵνα. The clause is an equative clause with the subject undefined, but the dative pronoun defines the person who is being referred to. The phrase γίνομαι εὖ may have the sense “be prosperous.”
καὶ ἔσῃ μακροχρόνιος – This the second part of the purpose clause, coordinated by καί. It also is an equative clause with a predicate adjective modifying the second person sing. subject.
ἐπὶ τῆς γῆς – An adverbial prepositional phrase with a locative sense expressing where this longevity will be enjoyed. The noun γῆ can mean “earth, land.” Given the additional information in Exodus and Deuteronomy the reference probably is to the land of Canaan, but Paul does not mention this and so the promise becomes much more general in sense, i.e., “on the earth,” and thus a general reference to longevity, rather than tied to convenant promise which incorporates the gift of land.
6:4 καὶ οἱ πατέρες, μὴ παροργίζετε τὰ τέκνα ὑμῶν ἀλλ’ ἐκτρέφετε αὐτὰ ἐν παιδείᾳ καὶ νουθεσίᾳ κυρίου.
καὶ οἱ πατέρες – Vocative, defining the subject of the imperative. The initial καί connects this command to the one expressed in v.1.
μὴ παροργίζετε τὰ τέκνα ὑμῶν – A prohibition formed on the present imperative and μή, indicating a general command. The imperative takes a direct object in the accusative case. The verb means “make angry.” Paul does not specify the cause of the anger. Note the previous cognate noun παροργισμός at 4:26.
ἀλλ’ ἐκτρέφετε αὐτὰ — Following a prohibition ἀλλ’ has an adversative sense, marking the action that should replace that which is prohibited. The present imperative verb occurred previously in 5:29. The antecedent of αὐτά is τέκνα.
ἐν παιδείᾳ καὶ νουθεσίᾳ κυρίου – The adverbial prepositional phrases define the means or instrument used in the nurturing. It might be that παιδείᾳ is the general means, i.e., training, and νουθεσίᾳ is more specific, i.e., admonitory instruction. If this is the case then καί might have an epexegetical function.