To understand this figure, you should know that Fructose-2,6-bisphosphate is an allosteric activator of PFK1 and, thus, controls the rate of conversion of Fructose-6-P to Fructose-1,6-biP, and, thus, the rate of glycolysis. Also, Fructose-2,6-bisphosphate is an allosteric inhibitor of Fructose-1,6-bisphosphatase and, thus, inhibits gluconeogenesis. When the concentration of Fructose-2,6-bisphosphate drops, glycolysis is no longer activated (becomes inhibited) and gluconeogenesis becomes activated (no longer inhibited).

When PFK-2/F-2,6-bisphosphatase is phosphorylated (P) by Protein kinase A in liver, PFK-2 is inhibited and F-2,6-bisphosphatase is activated.  The concentration of Fructose-2,6-bisphosphate is lowered so glycolysis is inhibited.

When PFK-2/F-2,6-bisphosphatase is phosphorylated (P*) by Protein kinase A in muscle, PFK-2 is activated and F-2,6-bisphosphatase is inhibited.  The concentration of Fructose-2,6-bisphosphate is raised so glycolysis is activated.

P and P* are two different sites on the PFK-2/F-2,6-bisphosphatase enzyme complex.  The addition of P inhibits PFK-2 in liver but the addition of P* activates PFK-2 in muscle.

I cannot explain the mechanism of activation of PFK-2 and glycolysis by insulin in muscle but it is the major control point.

Regulation of Phosphofructokinase-2/Fructose-2,6-bisphosphatase in Liver and Muscle

You might ask, how can I remember whether phosphorylation activates or inhibits an enzyme? Since I know that phosphorylation both activates many enzymes and inactivates many others, how can I remember? Specialists in metabolism don’t try but they can usually predict activation or inactivation of an enzymes by (1) knowing whether the pathway is active or inactive and (2) knowing whether the enzymes under consideration is being phosphorylated or dephosphorylated.

For example, is phosphokinase-2 active when phosphorylated in the liver? You know that, in the fed state, the enzyme must be active when glycolysis is running. You know that, in the fed state, insulin is high and that insulin usually inhibits the cyclic-AMP cascade and activates phosphatases that remove phosphate groups from enzymes phosphorylated by the cAMP cascade. Therefore, phosphokinase-2 is probably active when it is dephosphorylated. Furthermore, since you know that phosphokinase-2 and fructose-2,6-bisphosphatase are not active at the same time, you know that fructose-2,6-bisphosphatase is activated by phosphorylation.