**Core Concept**
Carcinoma breast spreads hematogenously, meaning through the bloodstream, to distant organs, a process known as metastasis. This involves the invasion of cancer cells into blood vessels, which can then carry them to other parts of the body.

**Why the Correct Answer is Right**
The correct answer is related to the venous drainage of the breast. The breast is drained by two main veins: the axillary vein and the internal thoracic vein. Cancer cells originating from the breast can invade these veins and spread to the lungs, a common site for breast cancer metastasis. The lung is a frequent site of metastasis due to the high blood flow and the presence of capillary beds that facilitate the seeding of cancer cells.

**Why Each Wrong Option is Incorrect**
**Option A:** Not provided, but we'll proceed with the next options.
**Option B:** Not applicable, as breast cancer can indeed spread hematogenously through the axillary vein, which is a major vein that drains the breast.
**Option C:** Not applicable, as the internal thoracic vein also drains the breast and is a potential route for hematogenous spread.

**Clinical Pearl / High-Yield Fact**
The most common sites for breast cancer metastasis are the lungs, bones, liver, and brain. The lung is the most common site due to the rich capillary network and high blood flow.

**Correct Answer:** Not provided, but assuming the format is complete, it would be: **Correct Answer: A. [Answer Text]**