How does the memory palace relate to the Major System?

They're complementary halves: the Major System supplies the images, the palace supplies the order and location.

The Major System turns numbers into concrete words/images (47 → "rake", 32 → "moon"). But a pile of images has no sequence. The palace solves that: you place each Major-System image at the next locus on your route. Recalling a long number becomes a walk past a rake on your doormat, a moon on your sofa, and so on. Memory athletes always run the two together — an image system to encode, a palace to sequence.