Catalyzes the reduction of the macrocycle of cobalt-precorrin-6A to cobalt-precorrin-6B. Co-precorrin-6B + NAD(+) = Co-precorrin-6A + H(+) + NADH Cofactor biosynthesis; adenosylcobalamin biosynthesis; cob(II)yrinate a,c-diamide from sirohydrochlorin (anaerobic route): step 7/10. Belongs to the precorrin-6x reductase family.