Neighbor B shares the distances it currently knows.
B shares its distances
B does not send A a full path here; it advertises the cost it currently knows for each destination.
B says C is close
B advertises C at cost 2. A has not decided yet whether that helps.
B says D is reachable
B advertises D at cost 4, which gives A its first finite-looking offer for D.
Summary
The next chapter adds A's link cost to each advertised distance and then compares the candidate against A's current table.
1+dB(dest)