The crowd crosses toward Capernaum seeking Jesus, and John eventually tells readers that Jesus taught these things in the synagogue there. Capernaum was an important Galilean lakeside settlement already central to Jesus' ministry.
The synagogue provides the social and religious setting for the discourse.
First-century synagogues served as places of communal assembly, prayer, Scripture reading, teaching, and discussion. Archaeological remains at Capernaum include a prominent later limestone synagogue built over earlier remains; the visible structure should not simply be identified as the exact building in which Jesus taught.
The existence of an earlier synagogue setting at Capernaum is nevertheless historically plausible and consistent with the Gospel traditions.
The setting reminds readers that Jesus' teaching about bread from heaven develops inside Jewish scriptural conversation, not outside it. Manna, Moses, the fathers, and divine teaching all belong naturally in a synagogue discourse.
The location also makes the division that follows more concrete: difficult claims about Jesus are heard and debated within a gathered community.