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What is The Co-enzyme required for the synthesis of fatty acid synthesis is: and explain in detail?
The Main Source of NADPH for Lipogenesis Is the Pentose Phosphate Pathway.
The pentose phosphate pathway is an alternative route for the metabolism of glucose. It does not lead  to formation of ATP but has two major functions:

The formation of NADPH for synthesis of fatty acids and steroids, and maintaining reduced  glutathione for anti- oxidant activity.
The synthesis of ribose for nucleotide and nucleic acid formation.

Ref:Harper's Illustrated Biochemistry 30th Edition 196