**Core Concept**
The liver plays a crucial role in detoxification, metabolism, and protein synthesis. After a hepatic resection, the liver's ability to regenerate and maintain its function is compromised, making it essential to assess the remaining liver's capacity to perform these critical functions.

**Why the Correct Answer is Right**
The most important hepatic function to consider after hepatic resection is the liver's ability to synthesize **coagulation factors**. The liver is responsible for producing most of the coagulation factors, including prothrombin, fibrinogen, and factor VII, which are essential for blood clotting. After a hepatic resection, the liver's reduced ability to synthesize these factors can lead to coagulopathy, which can increase the risk of bleeding and other complications.

**Why Each Wrong Option is Incorrect**
**Option A:** While the liver's detoxification function is crucial, it is not the most important function to consider after hepatic resection, as the liver's ability to regenerate and maintain its detoxification function is relatively preserved.

**Option B:** The liver's metabolic function, including gluconeogenesis and glycogen synthesis, is also important but not as critical as coagulation factor synthesis in the immediate postoperative period.

**Option C:** The liver's role in protein synthesis is essential, but it is not the most important function to consider after hepatic resection, as the liver's ability to regenerate and maintain its protein synthesis function is relatively preserved.

**Clinical Pearl / High-Yield Fact**
After a hepatic resection, it is essential to monitor the patient's coagulation status closely, including prothrombin time (PT), partial thromboplastin time (PTT), and fibrinogen levels, to prevent and manage coagulopathy.

**Correct Answer:** C. Coagulation factor synthesis.