In liver, phosphorylated PFK2 phosphatase activity is elevated and F2,6BP is converted to F6P.In this case, the body is starving so the liver is trying to release Glucose into the blood stream using Glycogenolysis and Gluconeogenesis. This step prevents the liver from attempting to metabolizing all of the Glucose it is trying to release. F2,6BP drives the formation of F1,6BP and therefore glycolysis. The opposite conditions are true in both cell types in the well fed state. Glucose is high, glucagon falls, cAMP doesn't accumulate so protein Kinase is not activated.
All glucose is dietary so liver can generate energy required to store excess.
Glucose supplies are high so any glucose taken up can be used to repleish stores spent during fastind. This assures that if the F6P is not being used and is just accumulating, glycolysis will be driven forward and ATP made. If you remember in Hb allostery, this is the compound which decreases the affinity of Hb for Oxygen and therefore promotes its unloading in the tissues. Therfore, it is needed at high concentrations in RBCs. This is the step which requires NAD as explained in the anerobic glycolysis section above.