To find intercepts with axes for Miller indices, one must determine the coordinates for the given directions in 3D space. The discussion includes attempts to calculate the indices for two directions, with initial values provided for both. Clarifications were made regarding the terminology, noting that "x, y, z components" is the standard term in American English, while "indices" is used in British English. The use of the Pythagorean theorem was suggested for justifying distances in calculations. Overall, the conversation revolves around understanding how to accurately represent and calculate Miller indices in three-dimensional geometry.