**Core Concept**
Invasive ductal carcinoma with skin involvement and axillary lymph node metastasis indicates locally advanced disease. The presence of skin involvement (inflammatory breast cancer features) and mobile axillary lymph nodes suggests a high tumor burden, necessitating systemic therapy before surgery to reduce tumor size and improve outcomes.

**Why the Correct Answer is Right**
In patients with locally advanced breast cancer, especially with skin involvement or axillary node metastasis, neoadjuvant chemotherapy is the standard initial management. It reduces tumor size, improves pathologic response, and enables more accurate staging. For this 40-year-old female with a 4 cm lesion and axillary lymph node involvement, neoadjuvant chemotherapy is preferred over immediate surgery. It also allows for assessment of response before definitive surgery, which may influence the surgical approach (e.g., choice between mastectomy or breast-conserving surgery).

**Why Each Wrong Option is Incorrect**
Option A: Radiotherapy is a local treatment used after surgery or for palliation, not the initial management in advanced cases. It does not address systemic disease or reduce tumor burden.
Option C: Modified radical mastectomy is a definitive surgical intervention, not the initial step. It is performed after neoadjuvant therapy to assess response and ensure complete removal.
Option D: Simple mastectomy lacks the benefit of systemic therapy and is not indicated in patients with nodal involvement or skin involvement. It is not the first-line approach in locally advanced disease.

**Clinical Pearl / High-Yield Fact**
In patients with locally advanced or node-positive invasive ductal carcinoma, neoadjuvant chemotherapy is the initial treatment to shrink tumors and improve survival, especially when skin involvement is present. This approach is part of the NCCN and ASCO guidelines for stage IIIB/C disease.

✓ Correct Answer: B. Neo-adjuvant chemotherapy