When he arrives at Mr. Been's, he notes the correct time.
When he leaves Mr. Been's he notes the time once more. Thus, he knows how long he has been there, and the precise time upon his departure.
When he checks his own clock, all Mr. Leen has to do is subtract the time he spent at Mr. Been's. This gives him his total walking time. If he halves this, he then has the total time it takes to make the trip one-way. He adds this time to the time he noted on Mr. Been's clock upon leaving, and he gets the current time.
For example: He sets his own (incorrect) clock to 12:00, walks to Mr. Been's, and notes that the accurate time is 10:30. He spends 2 hours there, and upon leaving notes that the time is 12:30.
When he arrives home, his own clock reads 3:00. Three hours have passed since he left the house.
Two hours were spent at Mr. Been's, which means that 1 hour was spent walking round trip. Thus, one leg of the trip takes 30 minutes. Since he left Mr. Been's at 12:30, he sets his clock for 1:00.