Jamieson, Fausset and Brown on Hebrews 6:18

18. immutable--Translate, as in He 6:17, "unchangeable."

impossible ... to lie--"ever to lie"; this is the force of the Greek aorist [Alford]. His not being able to deny Himself is a proof, not of weakness, but of strength incomparable.

consolation--under doubts and fears, and so "encouragement," literally, "exhortation."

fled for refuge--as if from a shipwreck; or, as one fleeing to one of the six cities of refuge. Kadesh, that is, holy, implies the holiness of Jesus, our Refuge. Shechem, that is, shoulder, the government is upon his shoulder (Is 9:6). Hebron, that is, fellowship, believers are called into the fellowship of Christ. Bezer, that is, a fortress, Christ is so to all who trust in Him. Ramoth, that is, high, for Him hath God exalted with His right hand (Ac 5:31). Golan, that is, joy, for in Him all the saints are justified and shall glory.

lay hold upon the hope--that is, the object of our hope, as upon a preservative from sinking.

set before us--as a prize for which we strive; a new image, namely, the race course (He 12:1, 2).