**Core Concept**
The **TNM staging system** is used to classify the extent of spread of cancer, with T describing the size of the tumor, N describing the presence and extent of lymph node involvement, and M describing the presence of metastasis. In breast cancer, the size of the tumor and the involvement of axillary lymph nodes are crucial for staging.

**Why the Correct Answer is Right**
A 6 cm breast lump with enlarged and fixed axillary lymph nodes on the ipsilateral side indicates a significant tumor size (T) and lymph node involvement (N). The tumor size is T3, as it exceeds 5 cm, and the fixed axillary lymph nodes indicate N2 disease, as mobility is impaired.

**Why Each Wrong Option is Incorrect**
**Option A:** Incorrect because it does not accurately reflect the tumor size or the extent of lymph node involvement.
**Option B:** Incorrect as it may not fully capture the extent of lymph node fixation.
**Option C:** Incorrect because the description does not match the clinical findings presented.

**Clinical Pearl / High-Yield Fact**
Remember, in the TNM staging system for breast cancer, the size of the tumor and the status of the axillary lymph nodes are critical for determining the stage and guiding treatment. Fixed axillary lymph nodes suggest a more advanced stage.

**Correct Answer:** C. T3 N2 M0