ἀργυρίου ἢ χρυσίου ἢ ἱματισμοῦ οὐδενὸς ἐπεθύμησα· (Acts 20:33 WH)
You will notice that all nouns in this verse occur in the genitive case, and so does the adjective οὐδενὸς. As for the verb, it comes at the end: ἐπεθύμησα. James A. Brooks and Carlton L. Winbery (Syntax of New Testament Greek, 20) explain that the construction is the genitive of root idea, wherein the verbs take genitive nouns as their objects.
A question that also preoccupies my mind is why Paul spoke this way. What scriptural antecedents influenced his view of covetousness? Obvious candidates are Exodus 20:17 and Deuteronomy 5:21: both verses contain the tenth commandment of the Mosaic Decalogue.
οὐκ ἐπιθυμήσεις τὴν γυναῖκα τοῦ πλησίον σου οὐκ ἐπιθυμήσεις τὴν οἰκίαν τοῦ πλησίον σου οὔτε τὸν ἀγρὸν αὐτοῦ οὔτε τὸν παῖδα αὐτοῦ οὔτε τὴν παιδίσκην αὐτοῦ οὔτε τοῦ βοὸς αὐτοῦ οὔτε τοῦ ὑποζυγίου αὐτοῦ οὔτε παντὸς κτήνους αὐτοῦ οὔτε ὅσα τῷ πλησίον σού ἐστιν (Exodus 20:17 LXX)
οὐκ ἐπιθυμήσεις τὴν γυναῖκα τοῦ πλησίον σου οὐκ ἐπιθυμήσεις τὴν οἰκίαν τοῦ πλησίον σου οὔτε τὸν ἀγρὸν αὐτοῦ οὔτε τὸν παῖδα αὐτοῦ οὔτε τὴν παιδίσκην αὐτοῦ οὔτε τοῦ βοὸς αὐτοῦ οὔτε τοῦ ὑποζυγίου αὐτοῦ οὔτε παντὸς κτήνους αὐτοῦ οὔτε ὅσα τῷ πλησίον σού ἐστιν (Deuteronomy 5:21 LXX)
Moreover, the teachings of Jesus (an observant Jew) supplied Paul with the needed impetus to avoid coveting anyone's silver, gold or garb (Luke 12:15). In the Sermon on the Mount and when telling the parable of Lazarus and the rich man, Jesus emphasized the vital necessity of eschewing covetousness (Matthew 6:24-34; Luke 16:14).
Many verses could be summoned to demonstrate Jehovah's view of covetousness, but one scriptural passage that also catches my eye is Exodus 3:22: αἰτήσει γυνὴ παρὰ γείτονος καὶ συσκήνου αὐτῆς σκεύη ἀργυρᾶ καὶ χρυσᾶ καὶ ἱματισμόν καὶ ἐπιθήσετε ἐπὶ τοὺς υἱοὺς ὑμῶν καὶ ἐπὶ τὰς θυγατέρας ὑμῶν καὶ σκυλεύσετε τοὺς Αἰγυπτίους (LXX)
Again, we see the mention of silver, gold, and garb. While it may be too much to ask whether Paul had this verse in mind as he uttered the words of Acts 20:33, it is not a stretch to assert that he was familiar with Exodus 3:22. Lastly, Achan's confession likely is a candidate for Paul's dogged refusal to covet anyone's material possessions: εἶδον ἐν τῇ προνομῇ ψιλὴν ποικίλην καλὴν καὶ διακόσια δίδραχμα ἀργυρίου καὶ γλῶσσαν μίαν χρυσῆν πεντήκοντα διδράχμων καὶ ἐνθυμηθεὶς αὐτῶν ἔλαβον καὶ ἰδοὺ αὐτὰ ἐγκέκρυπται ἐν τῇ γῇ ἐν τῇ σκηνῇ μου καὶ τὸ ἀργύριον κέκρυπται ὑποκάτω αὐτῶν (Joshua 7:21 LXX)
Compare 2 Kings 7:8.