**Core Concept**
Tuberous sclerosis is a genetic disorder characterized by the growth of non-cancerous tumors in various parts of the body, including the kidneys, liver, and brain. These tumors are caused by mutations in the TSC1 or TSC2 genes, leading to abnormal cell growth and organ dysfunction.

**Why the Correct Answer is Right**
The clinical presentation of left-sided flank pain, mental retardation, and the ultrasound findings of a hyperechoic lesion in the right kidney and multiple lesions in the liver are classic for tuberous sclerosis. The CT examination showing -50 to -80 HU density of these lesions is consistent with angiomyolipomas, a type of benign tumor that is commonly found in the kidneys of individuals with tuberous sclerosis. These tumors are composed of blood vessels, smooth muscle cells, and fat, which can lead to a characteristic low density on CT scans.

**Why Each Wrong Option is Incorrect**
**Option A:** Hereditary hemangioblastoma is a type of benign tumor that occurs in the retina, spinal cord, and cerebellum, but it is not typically associated with kidney or liver lesions.
**Option B:** Autosomal recessive polycystic kidney disease (ARPKD) is a genetic disorder characterized by the growth of cysts in the kidneys, but it is not typically associated with liver lesions or the characteristic CT findings seen in tuberous sclerosis.
**Option D:** von Hippel-Lindau syndrome is a genetic disorder characterized by the growth of tumors in the kidneys, pancreas, and other organs, but it is not typically associated with the same type of kidney and liver lesions seen in tuberous sclerosis.

**Clinical Pearl / High-Yield Fact**
Tuberous sclerosis is an autosomal dominant disorder, meaning that a single copy of the mutated gene is sufficient to cause the condition. Individuals with tuberous sclerosis are at increased risk of developing kidney failure, seizures, and other complications, and may require regular monitoring and management to prevent these outcomes.

✓ Correct Answer: A. Tuberous sclerosis