Step 1: Reduced glutathione (GSH) neutralises hydrogen peroxide and other free radicals through the enzyme glutathione peroxidase, in the process becoming oxidised glutathione (GSSG).
Step 2: To keep working as an antioxidant, GSSG must be converted back to GSH by glutathione reductase. This enzyme uses NADPH as the reducing agent.
Step 3: NADPH is built on the NADP coenzyme, which is derived from niacin (vitamin B3). Without an adequate niacin supply, NADPH cannot be generated and glutathione cannot be regenerated for repeated antioxidant action. Hence niacin is the vitamin required.
Step 4: Vitamins E and C are themselves antioxidants but are not needed to recycle glutathione, and vitamin A is unrelated to this cycle, so they are incorrect for this question.