That they may know that this is thy hand - That this has been done by thee; that it has all occurred under thy direction, or has been ordered by thee. The reference seems to be particularly to God’s interposition: “Let it be manifest to all that thou hast interposed in my behalf; that thou hast undertaken for me; that thou art my Friend.” He desired an interposition from God that he might be vindicated before all his enemies.
That thou, Lord, hast done it - Let it be such an interposition that it will be manifest to all that no other one but God could have done this.