“the Amorites that lived beyond the Jordan.” The phrase “beyond the Jordan” can refer to either east (Deut. 3:8; Josh. 24:8) or west (Deut. 3:20; 11:30) of the Jordan River depending on the context or the location of the speaker. In this case, the Amorites lived on the east side of the Jordan, in the Transjordan (Num. 21:21-35).
“I gave them into your hand.” An idiom meaning that God put them under the power (“hand”) of Israel.
“I destroyed them.” Israel did the fighting, but the battle was fought with God’s power and God gave the victory.