**Core Concept:** Paneth cells are a type of enteroendocrine cell located in the intestinal crypts. They possess prominent eosinophilic secretory granules, which contain various antimicrobial peptides and proteins that play a crucial role in maintaining gut homeostasis and host defense against pathogens.

**Why the Correct Answer is Right:** The correct answer is **C**. The prominent eosinophilic secretory granules in Paneth cells contain a protein called lysozyme, which is an enzyme that degrades bacterial cell walls and prevents bacterial overgrowth in the gut. Lysozyme plays a significant role in maintaining intestinal barrier function, preventing bacterial translocation, and combating infection.

**Why Each Wrong Option is Incorrect:**

A. **Option A (Bacterial Peptidases and Proteases)**: These are enzymes that break down proteins and peptides, not secreted from Paneth cells.
B. **Option B (Duodenal Hormones)**: Paneth cells are not involved in the secretion of hormones like insulin or glucagon, which are secreted by alpha and beta cells of the pancreas.
D. **Option D (Peptide Hormones)**: While Paneth cells do secrete peptide hormones, the primary function of Paneth cells is related to antimicrobial peptides and proteins, not peptide hormones.

**Clinical Pearl / High-Yield Fact:** The prominent eosinophilic secretory granules in Paneth cells are a key component of the gut-associated lymphoid tissue (GALT), which comprises the Peyer's patches and mucosa-associated lymphoid tissue (MALT) in the small intestine. Paneth cells, along with other immune cells, form the basis of the intestinal immune system and contribute to the defense mechanisms against pathogens and the maintenance of gut homeostasis.

**Correct Answer:** C. Lysozyme