If the path difference for points on the first nodal line is 4 cm, then the wavelength would be 6 cm. Now one notices that y is inversely related to d. This condition leads to constructive interference and an antinodal point is formed. This condition leads to destructive interference and a nodal point is formed. This condition leads to constructive interference and an antinodal point is formed.
Antinodes result from constructive interference.
Nodes result from destructive interference. The central line on the interference pattern is a nodal line. Points on nodal lines would be represented by bright spots if projected onto a screen. The path difference for points on the central antinodal line would be 0. The path difference for points on the first antinodal line would be 1 cm.