Exegesis:

katanoēsas … autōn tēn panourgian ‘seeing through their trickery.’ For katanoeō cf. on 12.24; here it means ‘to see through,’ ‘to perceive what is hidden.’

panourgia ‘trickery,’ ‘cunning.’

(V. 24) deixate moi dēnarion ‘show me a denarius,’ cf. on 7.41.

tinos echei eikona kai epigraphēn ‘whose likeness and inscription does it have?’ tinos goes with both eikona and epigraphēn.

eikōn ‘image,’ ‘likeness,’ ‘head’ on coin.

epigraphē (also 23.38) ‘inscription,’ ‘legend’ on a coin.

(V. 25) hoi de eipan, Kaisaros ‘they said, Caesar’s.’ In Nestle these words belong to v. 24 (cf. Revised Standard Version and other versions).

toinun apodote ta Kaisaros Kaisari ‘then give Caesar what belongs to Caesar.’ toinun introduces a strong inference. apodidōmi ‘to give, or to pay what is due.’ ta Kaisaros lit. ‘the things of Caesar,’ i.e. ‘what is due to Caesar,’ ‘what Caesar is entitled to receive.’

Translation:

He, i.e. Jesus, may have to be specified; similarly in v. 25.

Perceived their craftiness, or “saw through their trick” (New English Bible); in Sranan Tongo the idiom is ‘bored through their head and came to know their trick,’ in Javanese ‘not ignorant of their deceit.’

(V. 24) Coin, or ‘piece of silver, or, money,’ ‘silver coin,’ see references on “denarii” in 10.35; cultural equivalents as mentioned there are not advisable here, because the reference is not to the value but to the object and its historical details. Sometimes a coin of the same value cannot be used because it has no effigy or legend, but one of different value has the details required and hence is the closest natural equivalent, e.g. in Sranan Tongo.

Whose likeness and inscription has it, or with a syntactic shift, ‘who is portrayed on it? Whom does the inscription mention?’ (cf. Leyden). Likeness, or “portrait” (The Four Gospels – a New Translation) “face” (Good News Translation). Inscription, or, ‘writing’ (Batak Toba), ‘stamp/seal’ (Bahasa Indonesia), “name” (Good News Translation), ‘name mark’ (Javanese), ‘written mark.’

Caesar’s, or, ‘those of (or, they belong to, or, the likeness and inscription are of) the Emperor’; or, ‘the Emperor’ (Leyden, cf. above). The answer may have to be introduced by an affirmative expression, without which it would sound impolite, ‘indeed (or, yes, or, you are right), Caesar’s’ (Javanese, Sundanese).

(V. 25) Then, or ‘well, then,’ ‘because that is so,’ ‘for that reason.’

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.