The sense is that the Reubenites and Gadites were to possess the district from the Jabbok on the north to the Arnon on the south, including the middle part of the valley of the Arnon, and the territory ("coast" or "border") thereto pertaining.

And unto the Reubenites, and unto the Gadites,.... The tribes of Reuben and Gad:

I gave from Gilead even unto the river Arnon: see Deuteronomy 3:12.

half the valley and the border; or rather half the river, the river Arnon; and so it is rendered "the middle of the river", in Joshua 12:2 and so here the middle of the torrent by the Vulgate Latin and Septuagint versions, and by Onkelos:

even unto the river Jabbok, which is the border of the children of Ammon; beyond which the land given to the tribes of Reuben and Gad reached not; see Deuteronomy 2:37.

And unto the Reubenites and unto the Gadites I gave from Gilead even unto the river Arnon half the valley, and the border even unto the river {f} Jabbok, which is the border of the children of Ammon;

(f) Which separates the Ammonites from the Amorites.

3:16 Half the valley - Or rather to the middle of the river: for the word rendered half signifies commonly middle, and the same Hebrew word means both a valley and a brook or river. And this sense is agreeable to the truth, that their land extended from Gilead unto Arnon, and, to speak exactly, to the middle of that river; for as that river was the border between them and others, so one half of it belonged to them, as the other half did to others, Jos 12:2. The same thing is expressed in the same words in the Hebrew which are here, though our translators render the self - same words there, from the middle of the river, which here they render, half of the valley. There the bounds of Sihon's kingdom, which was the same portion here mentioned as given to Reuben and Gad, are thus described, from Aroer, which is upon the bank of the river of Arnon, and from the middle of the river, and from half Gilead, even unto the river Jabbok, which is the border of the children of Ammon.

16. from Gilead-that is, not the mountainous region, but the town Ramoth-gilead,

even unto the river Arnon half the valley-The word "valley" signifies a wady, either filled with water or dry, as the Arnon is in summer, and thus the proper rendering of the passage will be-"even to the half or middle of the river Arnon" (compare Jos 12:2). This prudent arrangement of the boundaries was evidently made to prevent all disputes between the adjacent tribes about the exclusive right to the water.

3:12-20 This country was settled on the Reubenites, Gadites, and half the tribe of Manasseh: see Nu 32. Moses repeats the condition of the grant to which they agreed. When at rest, we should desire to see our brethren at rest too, and should be ready to do what we can towards it; for we are not born for ourselves, but are members one of another.