Steroid hormones are nonpolar molecules that can travel across the hydrophobic (or nonpolar) interior of the plasma membrane whereas peptide hormones are polar molecules that cannot travel across the hydrophobic interior. The question states that the hormone cannot enter the cell. This means that it cannot traverse the plasma membrane and, therefore, must be a peptide hormone. A peptide is made up of several amino acids. There are polar and nonpolar amino acids. Since they are polar, peptide hormones must have at least a few polar amino acids. These polar amino acids can be positively charged, negatively charged, or uncharged. There are twelve polar amino acids, five of which are charged (aspartic acid, glutamic acid, histidine, lysine, and arginine). Aspartic acid and glutamic acid are negatively charged at physiologic pH, whereas the other three are positively charged. A molecule that forms clumps in water is hydrophobic and nonpolar. Since we are dealing with a peptide hormone, the hormone will dissolve and not form clumps in water. A steroid hormone, on the other hand, is nonpolar and will form clumps in water.

A hormone is a signaling molecule that binds to a receptor and initiates a signaling cascade inside the cell. The receptor for a hormone can be found on the periphery of the cell (on plasma membrane) or inside the cell (cytoplasm or nucleoplasm). A steroid hormone is nonpolar and can traverse the hydrophobic interior of the plasma membrane whereas a peptide hormone is polar and cannot traverse the hydrophobic interior; therefore, a steroid hormone will have its receptor inside the cell whereas a peptide hormone will have its receptor on the plasma membrane. The question is asking us to find the polar, peptide hormone (because its receptor will be found on the plasma membrane, not in cytoplasm). To answer this question, we need to know which amino acids are polar. Recall that there are twelve polar amino acids. They are serine, threonine, cysteine, tyrosine, asparagine, glutamine, aspartic acid, glutamic acid, histidine, lysine, and arginine; therefore, the hormone containing phenylalanine, histidine, and methionine is most likely to be polar. The rest of the hormones have nonpolar amino acids only.

Peptide hormones are polar molecules that cannot traverse the plasma membrane. Recall that plasma membranes have a hydrophobic interior. Since peptide hormones are polar, they cannot travel through this hydrophobic interior of the plasma membrane; therefore, peptide hormones signal cells by binding to receptors on the plasma membrane. There are several types of hormone receptors on the membrane, including G protein coupled receptors and receptor tyrosine kinases. Upon binding, the receptors activate themselves and other intracellular molecules called second messengers. This leads to a signaling cascade that ultimately results in upregulation or downregulation of processes inside the cell. Second messenger molecules facilitate the amplification and propagation of signal throughout the cell. Cyclic adenosine monophosphate, or cAMP, is one of the most common second messenger molecules; therefore, all three molecules listed in this question are involved in peptide hormone pathway.

Insulin promotes the translocation of GLUT-4 receptors to the cell surface through cell signaling triggered by its binding to cell surface insulin receptors. GLUT-2 transporters are insulin-independent and are found in tissues like the pancreas and liver where immediate glucose sensing is important for whole body function (The pancreas needs to sense glucose so it can secrete insulin for the rest of the body. Imagine if the pancreas itself needed insulin.)

Glucagon and epinephrine are typically thought of as having catabolic effects; however, their purpose is to increase the availability of fuel substrates to extra-hepatic tissues during the fasting state or during fight or flight situations, respectively. So, while many of their effects like glycogenolysis and lipolysis conform to this pattern, they also induce the anabolic process of gluconeogenesis in the liver to increase the availability of glucose to other tissues.

ACTH is regulated by a negative feedback loop, in which ACTH secretion stimulates production of cortisol, but this feeds back on to the hypothalamus to inhibit the production of corticotropin-releasing hormone (CRH). CRH is a positive regulator of ACTH production, so a decrease in CRH ultimately results in a decrease in ACTH. 

Phospholipase C normally breaks down phosphatidylinositol (3,4,5)-trisphosphate (PIP3) into diacylglycerol (DAG) and inositol 1,4,5-triphosphate (IP3). This cascade eventually increases cytosolic calcium levels through its release from the endoplasmic reticulum and from the extracellular fluid. Malfunction in this enzyme results in PIP3 not being broken down.

Insulin is a peptide hormone that is released in the fed state. Thus, it promotes glucose storage and DNA replication, but decreases glycogen breakdown and the release of glucose.

Glucagon is a peptide hormone that is released in the fasted state. It stimulates macromolecule breakdown and the production and subsequent release of glucose into the blood stream. It is synthesized and released from the alpha-cells in the pancreatic islets.

Insulin release is induced by incretins in the blood (ex. GLP-1), and a high carbohydrate meal. Incretins are metabolic hormones that stimulate a decrease in blood glucose. Growth hormone does not cause an increase in blood insulin.