Exegesis:

tauta gar panta ta ethnē tou kosmou epizētousin ‘all these things the peoples of the world are pursuing’ (taking tauta panta together), or ‘these things all the people of the world are pursuing’ (taking panta ta ethnē together), preferably the former. tauta panta refers to such things as eating and drinking. ta ethnē refers to the peoples of the world that live outside the covenant-relationship between God and Israel. The present tense of epizētousin is habitual. epizēteō, cf. on 4.42.

humōn de ho patēr ‘your father,’ with continuing emphasis on humōn, ‘you as distinct from the peoples of the world.’

oiden hoti chrēzete toutōn ‘knows that you need these things.’ toutōn refers to the same things as tauta panta. chrēzō, cf. on 11.8.

Translation:

The nations of the world has the same reference meaning as “the Gentiles” in 2.32 (which see); it may be translated, ‘the heathen’ (Toraja-Sa’dan), “the pagan world” (The Four Gospels – a New Translation), ‘the other (or, non-Jewish) peoples in the world.’

Your Father, cf. on 6.36.

You need them, i.e. you are in need/want of them, or since the implied reference is to food, ‘you live-on those things’ (Toraja-Sa’dan).

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.