John Gill Commentary Numbers 22:36

"And when Balak heard that Balaam was come, he went out to meet him unto the City of Moab, which is on the border of the Arnon, which is in the utmost part of the border." — Numbers 22:36 (ASV)

And when Balak heard that Balaam was come
Messengers being sent to acquaint him with it, either by Balaam, or by the princes:

he went out to meet him ;
overjoyed at the news that his princes had succeeded, and to show him respect, and do him honour, and all to encourage him to do his utmost for him:

unto a city of Moab, which is in the border of Arnon, which is in the
utmost coast ;
by the situation of it, being on the border of the river Arnon, which river was in the extreme parts of Moab, and divided between the Moabites and Amorites, it is generally thought to be the city Ar, called "Ar of Moab", see (Numbers 21:13Numbers 21:28) , and the king coming to meet Balaam so far as the uttermost border of his dominions showed the greater respect to him.