**Core Concept**
The presence of an abdominal mass and ascites in a 51-year-old female patient is suggestive of ovarian cancer, which is a type of malignancy that arises from the epithelial cells of the ovaries. This condition often presents with advanced disease, including metastasis to the peritoneal cavity, leading to ascites and potentially a palpable abdominal mass.

**Why the Correct Answer is Right**
The correct answer is related to the tumor marker that is commonly elevated in ovarian cancer. CA-125 is a mucin-like glycoprotein that is expressed on the surface of ovarian cancer cells and is shed into the peritoneal fluid, leading to elevated levels in the blood. This makes it a useful marker for diagnosing and monitoring ovarian cancer. The elevated levels of CA-125 in this patient's blood would be consistent with the diagnosis of ovarian cancer.

**Why Each Wrong Option is Incorrect**
**Option A:** CA-19-9 is a tumor marker that is associated with pancreatic cancer, not ovarian cancer. While CA-19-9 can be elevated in various types of cancer, it is not a specific marker for ovarian cancer.

**Option B:** CEA (Carcinoembryonic Antigen) is a tumor marker that is elevated in various types of cancer, including colorectal, lung, and breast cancer. However, it is not specific to ovarian cancer and can be elevated in other conditions as well.

**Option C:** AFP (Alpha-fetoprotein) is a tumor marker that is elevated in certain types of cancer, including hepatocellular carcinoma and germ cell tumors of the ovary. However, it is not a specific marker for epithelial ovarian cancer.

**Option D:** LDH (Lactate Dehydrogenase) is an enzyme that is elevated in various types of cancer, including lymphoma and germ cell tumors of the ovary. However, it is not a specific marker for epithelial ovarian cancer.

**Clinical Pearl / High-Yield Fact**
CA-125 is not specific to ovarian cancer and can be elevated in other conditions, such as pregnancy, endometriosis, and pelvic inflammatory disease. However, in the context of a patient with an abdominal mass and ascites, an elevated CA-125 level would be highly suggestive of ovarian cancer.

**Correct Answer:** C.