A novel inbred maize line designated PHB6R and seed, plants and plant parts thereof. Methods for producing a maize plant that comprise crossing inbred maize line PHB6R with another maize plant. Methods for producing a maize plant containing in its genetic material one or more traits introgressed into PHB6R through backcross conversion and/or transformation, and to the maize seed, plant and plant part produced thereby. Hybrid maize seed, plant or plant part produced by crossing the inbred line PHB6R or an introgressed trait conversion of PHB6R with another maize line. Inbred maize lines derived from inbred maize line PHB6R, methods for producing other inbred maize lines derived from inbred maize line PHB6R and the inbred maize lines and their parts derived by the use of those methods.