(Words in italics are words not found in the Hebrew text but need to be supplied in the target language, English. Words underlined are a Hebrew idiom. Words in brackets  are in the text but not needed in the English translation to make sense of the text.)
His brothers went to shepherd their father’s flock in Shechem. And Israel said to Joseph, “Are your brothers not shepherding in Shechem? Come, let me send you to them.” And Joseph said to him, “Here I am!” And Israel said to him, “Go, then. See the welfare of your brothers and the welfare of the flock, then bring me word.” So, he sent him from the valley of Hebron, and he went to Shechem. Then a man found him, and behold, he was wandering in the field, and the man asked him, “What are you seeking?” Joseph said, “I am seeking my brothers. Please tell me where they are shepherding.” The man said, “They travelled from this place, for I heard them saying, ‘Let us go to Dothan.'” So, Joseph went after his brothers and found them in Dothan.
There’s not much to comment on here besides the places Joseph travelled. He begins in the valley of Hebron and travels first to Shechem, where his brothers are shepherding. This was a 50-mile hike along the rocky hills of Canaan, which would’ve been no easy hike. Going from Shechem to Dothan would be another 16- 17-mile hike. So, the task of finding his brothers was a several days’ journey.
This perilous journey would also (falsely) justify the brothers’ later action of falsifying the story of Joseph getting eaten by wild animals. That is, a person getting eaten alive by wild animals along this journey would not be an uncommon occasion.
It is also not surprising that the man knew where his brothers were going. Word would’ve spread throughout the region that a sizable group of men were shepherding a flock in the fields. What this man was doing there, who knows? Perhaps he was simply passing through when he heard the brothers discussing going to Dothan.
Why did the brothers want to go to Dothan? We can only speculate. It’s possible they had business there, or perhaps they wanted to take a break from shepherding and blow off some steam. Sixteen to seventeen miles might seem too long of a distance to take a break, but Dothan would be the nearest city to Shechem. Why couldn’t they simply blow off steam at Shechem and stay near the flock? Again, who knows? Perhaps Dothan was a more bustling city than Shechem and had better markets. Shechem was also a considerable city of refuge, so that could be a reason of there not being very many social activities and, therefore, a boring place for young men.
This passage could be considered the rising action of Joseph’s story until its climax, when he is sold into slavery and spends considerable time in Egypt as a slave.