Luke 16:4 I am resolved what to do, that, when I am put out of the stewardship, they may receive me into their houses.
I know what I will do in order that, when I might change my position out of the management of this household, they might accept me into those households of their own.
What is lost in translation is the connection between the change from the management of one household to being welcomed into other households as a manager. The KJV makes it sound like his interest in in being entertained. This double meaning may be intentional.
"I am resolved" is a verb that means "to know", "to recognize", "make known", "to know carnally," and "to learn". Its translation as "resolved" is misleading. A simple, "I know" would capture it better.
The word translated as "what" means primarily "anything" or "anyone," but Jesus often uses it to start a question so it means "who", "what", or even "why". The sense is "I know something to do", but in English we would also say "what".
The Greek word translated as "to do" has the primary meaning of "making" or producing" something or "causing" or "rendering" as service. It describes a productive action. It is not as broad a word as the English "do", which covers all actions, productive or not. It is not an infinitive "to do" but an active verb in the future tense, "I will do". The sense might be closer to "how I will perform" or "how I will act".
The word translated as "that" is an adverb or a conjunction that starts a subordinate clause "there", "where," and "in order that."
The Greek word translated as "when" introduces a phrase that explains a certain condition so "whenever" or "since."
"I am put" is a Greek verb that Jesus only uses here. This is not the simple word that means "put". which is this word's root. It has a prefix that means "with" or "among". It generally means to change positions of things. It is in the passive form where it can mean to "stand among", and "change one's position". The later is clearly the meaning because of the words that follow, which refer to a position.
The Greek preposition translated as "of" means "out of" or "from."
"Stewardship" is a Greek noun that means "management of a household","husbandry", "thrift", "regulation", "transaction", "contract", and "operation". This is the female form of the noun "steward", referring to the discipline rather than the person.
"They may receive" is a word, which, when applied to people as it does here, means "to welcome", "to grant access," "give ear to, hear", or "to receive with hospitality. It also has a strong sense of "accept", and "approve". This is said in the context of someone who was slandered (Luke 16:1).
"Me" is the regular first-person pronoun in Greek.
The word translated as "into" means "into" a place, "towards" as a direction, "in regards to" a subject, and "up to" limits in time and measure.
"their" is a special reflexive pronoun that means "himself", "herself," and so on. When used in the possessive form, as here, the sense is "their own" not just "their", which is a much more common word.
The Greek word translated as "house," is any dwelling place but not exclusively a separate house. It means the household or clan that lives in the building as well.
ἔγνων (verb 1st sg aor ind act) "I am resolved," is ginosko which means "to learn to know", "to know by reflection or observation," and "to perceive."
τί (pro sg neut nom/acc) "What" is tis which can mean "someone", "any one", "everyone", "they [indefinite]", "many a one", "whoever", "anyone", "anything", "some sort", "some sort of", "each", "any", "the individual", "such," and so on. In a question, it can mean "who", "why," or "what."
ποιήσω, (verb 1st sg fut ind act) "To do" is poieo, which means "to make", "to produce", "to create", "to bring into existence", "to bring about", "to cause", "to render", "to consider", "to prepare", "to make ready," and "to do."
ἵνα (adv/conj) "That" is hina, which means "in that place", "there", "where", "when", "that", "in order that", "when," and "because."
ὅταν (adv/conj) "When" is from hotan, which means "whenever (as a condition)," and "since (as a cause)."
μετασταθῶ [unique](verb 1st sg aor subj pass) "I am put" is metahistemi, which means to "place in another way", "change", "remove from one place to another", "remove from oneself or from one's presence", and in passive to "stand among", and "change one's position".
ἐκ (prep) "Out of" is ek, which means 1) [of motion] "out of", "from", "by", "away from;" 2) [of place] "beyond", "outside of", "beyond;" 3) [of succession] "after", "from;" 4) [of rest] "on", "in," 5) [of time] "since", "from", "at", "in;" 5) [of materials] "out of", "made from."
τῆς οἰκονομίας [uncommon](noun sg fem gen) "Stewardship" is oikonomia, which means "management of a household","husbandry", "thrift", "regulation", "transaction", "contract", and "operation".
δέξωνταί (verb 3rd pl aor subj mid) "They may receive" is dechomai, which means "welcome", "accept," and "entertain" when applied to people and "take", "accept," and "receive" when applied to things.
με (noun sg masc acc) "Me" is eme, which means "I", "me", and "my".
εἰς (prep) "Into" is eis, which means "into (of place)," "up to (of time)", "until (of time)", "as much as (of measure or limit)", "as far as (of measure or limit)", "towards (to express relation)", "in regard to (to express relation)", "of an end or limit," and "for (of purpose or object)."
τοὺς οἴκους (noun pl masc acc) "House" is oikos, which means "house", "dwelling place", "room", "home", "meeting hall", "household goods", "substance," and "ruling family." It is any dwelling place but not exclusively a separate house.
ἑαυτῶν. (pro pl masc gen) "Their" is heautou, is a reflexive pronoun that means "himself", "herself", "itself" "themselves," and "ourselves." It is an alternative to autos.
The word translated as "they may receive" also means "to accept".