Here "hand" refers to control. Alternate translation: "He has given you control over the animals of the fields and the birds of the heavens" (See: [[rc://en/ta/man/jit/figs-metonymy]])
In the king's dream the statue's head represents the king. Alternate translation: "The golden head symbolizes you" or "The golden head is a symbol of you and your power" (See: [[rc://en/ta/man/jit/writing-symlanguage]])