Step 1: Identify the metabolic pathway: G6PD opens the pentose phosphate pathway, whose chief role is to generate NADPH for fatty-acid synthesis and for keeping glutathione reduced in red cells.
Step 2: Because the pathway exists to make NADPH, the dehydrogenase that starts it must hand its electrons to NADP+. G6PD oxidises glucose-6-phosphate and simultaneously converts NADP+ into NADPH.
Step 3: Sorting the cofactors helps: catabolic, energy-yielding dehydrogenases generally use NAD+ or FAD, whereas the reductive, biosynthetic ones use NADP+. FMN serves Complex I of the respiratory chain. G6PD clearly belongs to the NADP+-using, anabolic group, so options NAD, FAD and FMN are excluded.
Step 4: The required coenzyme is NADP.
\[\boxed{\text{NADP}}\]