Adam Clarke on Psalms 20:6

Now know I that the Lord saveth his anointed - These are probably the words of the priest after the victim had been consumed; and those signs had accompanied the offering, which were proofs of God's acceptance of the sacrifice; and, consequently, that the campaign would have a successful issue. David is God's anointed; therefore, he is under his especial care. He will hear him. David must continue to pray, and to depend on God; else he cannot expect continual salvation. David has vast multitudes of enemies against him; he, therefore, requires supernatural help. Because of this, God will hear him with the saving strength of his right hand.

The Hand of God is his power, the Right hand, his almighty power; the Strength of his right hand, his almighty power in action; the Saving strength of his right hand, the miraculous effects wrought by his almighty power brought into action. This is what David was to expect; and it was the prospect of this that caused him and his officers to exult as they do in the following verse.