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What is Which favours gluconeogenesis in the fasting state and explain in detail?
Acetyl CoA activation of pyruvate carboxylase

In starvation, glucagon secretion is increased.
Glucagon increases fatty acid mobilization and their oxidation to yield acetyl CoA, NADH and ATP. These compound inhibit the PDH complex and acetyl CoA stimulates pyruvate carboxylase. Thus, the available pyruvate is not converted to acetyl CoA but to oxaloacetate for gluconeogenesis.

About other options

Acetyl CoA carboxylase is the most important regulating enzyme in fatty acid synthesis. It is activated by citrate, which increases in concentration in the well-fed state (not during starvation).
Pyruvate kinase and phosphofructokinase-I are regulating enzymes in glycolysis. Their activity is inhibited during starvation.