These two phrases mean basically the same thing and are used together to emphasize that Yahweh saved them from their enemies. (See: [[rc://en/ta/man/translate/figs-parallelism]])
Here "hand" refers to power or control. Alternate translation: "the power of those who hated them" or "the control of those who hated them" (See: [[rc://en/ta/man/translate/figs-metonymy]])