Step 1: Sort the four molecules into the two hypothalamic feeding circuits. One circuit drives hunger (orexigenic) and the other suppresses it (anorexigenic). The correct answer must be the only orexigenic member.
Step 2: The POMC neuron products are appetite suppressors. From POMC come $\alpha$-MSH and the co-transmitter CART, both of which act on melanocortin receptors to curb feeding. Insulin reaches the hypothalamus as an adiposity signal and likewise dampens appetite.
Step 3: That leaves AGRP, the agouti-related peptide. Released by the NPY/AGRP neurons, it is a potent hunger signal: it antagonises the MC4 receptor, removing the brake that $\alpha$-MSH applies, and thereby pushes food intake up.
Step 4: Since three of four options reduce appetite and only AGRP raises it, AGRP is the answer. (Printed as AGPP by a typographical slip.)
\[\boxed{\text{AGRP}}\]