**Core Concept**
The diagnosis of palpable breast masses involves a combination of physical examination, imaging techniques, and sometimes histopathological evaluation. The most common procedure for diagnosing palpable breast masses relies on the principles of mammography and ultrasound, which help in characterizing the mass and determining its nature.

**Why the Correct Answer is Right**
The correct answer is **Mammography**. Mammography is a widely used imaging technique for breast cancer screening and diagnosis. It involves the use of low-energy X-rays to produce images of the breast tissue. The procedure is particularly useful for detecting small, non-palpable lesions and for differentiating between benign and malignant lesions. In the case of palpable breast masses, mammography helps in characterizing the mass, determining its size, shape, and margins, and assessing the presence of any calcifications or microcalcifications.

**Why Each Wrong Option is Incorrect**
**Option A:** Ultrasonography is a useful imaging technique for breast lesions, especially for women with dense breast tissue. However, it is not the most frequently used procedure for diagnosing palpable breast masses.

**Option B:** Magnetic Resonance Imaging (MRI) is a highly sensitive imaging technique for breast lesions, particularly for detecting lesions in women with a high risk of breast cancer. However, it is not the most commonly used procedure for diagnosing palpable breast masses.

**Option C:** Fine-needle aspiration cytology (FNAC) is a diagnostic procedure that involves the aspiration of cells from a breast mass using a fine needle. While FNAC can provide valuable information about the nature of a breast mass, it is not the most frequently used procedure for diagnosing palpable breast masses.

**Clinical Pearl / High-Yield Fact**
It is essential to note that the choice of imaging technique for diagnosing palpable breast masses depends on various factors, including the patient's age, breast density, and the presence of any symptoms or risk factors for breast cancer.

**Correct Answer:** B.