**Core Concept**
The extraction of maxillary third molars is a complex procedure due to the anatomical location and proximity to vital structures such as the inferior alveolar nerve, maxillary sinus, and nasal cavity. This procedure requires careful planning and execution to minimize complications.

**Why the Correct Answer is Right**
The most commonly encountered complication during the extraction of maxillary third molars is **injury to the inferior alveolar nerve**. This nerve runs through the mandibular canal and supplies sensation to the lower lip, chin, and lower teeth. During extraction, the nerve can be damaged, leading to numbness, tingling, or pain in the affected area. The risk of nerve injury is higher in maxillary third molar extractions due to the nerve's proximity to the extraction site.

**Why Each Wrong Option is Incorrect**
* **Option A:** **Dry socket** is a complication that can occur after any tooth extraction, but it is not the most commonly encountered complication during maxillary third molar extraction. Dry socket is characterized by the exposure of bone and nerve endings, leading to pain and discomfort.
* **Option B:** **Maxillary sinusitis** is a possible complication of maxillary third molar extraction, but it is not the most common complication. Maxillary sinusitis occurs when the sinus membrane is perforated or irritated during the extraction procedure.
* **Option C:** **Nasal cavity injury** is a rare complication of maxillary third molar extraction, but it is not the most common complication. Nasal cavity injury can occur if the nasal septum or nasal turbinates are damaged during the extraction procedure.

**Clinical Pearl / High-Yield Fact**
When extracting maxillary third molars, it is essential to carefully evaluate the patient's anatomy, including the position of the inferior alveolar nerve, to minimize the risk of nerve injury. This can be done using preoperative imaging studies such as panoramic radiographs or CBCT scans.

**Correct Answer: B. Maxillary sinusitis.**