Step 1: Gardner syndrome is a variant of familial adenomatous polyposis (FAP) defined by the combination of intestinal adenomatous polyps with prominent extra-intestinal features.
Step 2: The hallmark extra-intestinal features include multiple epidermoid (epidermal inclusion) cysts, osteomas (especially of the skull and mandible), desmoid tumors, lipomas, dental abnormalities and periampullary carcinomas.
Step 3: Why the others are wrong - Turcot syndrome links colonic polyposis with central nervous system tumors (medulloblastoma or glioblastoma). Peutz-Jeghers shows hamartomatous polyps with mucocutaneous pigmentation, not epidermoid cysts. Familial polyposis coli alone is purely intestinal without the skin and bone lesions.
Answer: Gardner's syndrome.