Here "hand" refers to the actions of Moses. Alternate translation: "was giving them deliverance through what he, Moses, was doing" (See: [[rc://en/ta/man/jit/figs-metonymy]])
The abstract noun "deliverance" can be translated using the verb "deliver." Alternate translation: "was delivering them" or "was rescuing them" (See: [[rc://en/ta/man/jit/figs-abstractnouns]])