The way a person lives is spoken of as if that person were walking on a path, and "to walk after" someone is a metonym for doing what that other person does or wants others to do. Alternate translation: "live obeying Yahweh" (See: [[rc://en/ta/man/translate/figs-metaphor]] and [[rc://en/ta/man/translate/figs-metonymy]])
These words all share similar meanings. Together they emphasize everything that Yahweh had commanded in the law. (See: [[rc://en/ta/man/translate/figs-doublet]])
The idiom "with all his heart" means "completely" and "with all his soul" means "with all his being." These two phrases have similar meanings. Alternate translation: "with all his being" or "with all his energy" (See: [[rc://en/ta/man/translate/figs-idiom]] and [[rc://en/ta/man/translate/figs-doublet]])