“carry them out.” That is the idea of the more clipped Hebrew text, “to do” them (cp. NET; “observe” them (TNK, NRSV); “you must obey them” (NLT); “follow them” (HCSB)). Using the word “may” or “might” (KJV; HCSB; ESV; NASB) gives the wrong impression in English because God did not give His commands so that we “might” keep them, but so that we “would” keep them. When it comes to obeying God, it is important that the English translation conveys the meaning of the text very well.
“are crossing over.” Israel was about to cross over the Jordan River and then fight and possess the Promised Land.