Okay, let's tackle this question. The question is about the nerve supply to the extensor hallucis longus muscle. I need to remember which nerve innervates this muscle.

First, I recall that the muscles in the lower leg are innervated by different nerves. The extensor hallucis longus is one of the muscles that extend the big toe. The common peroneal nerve splits into superficial and deep branches. The deep peroneal nerve, also known as the anterior tibial nerve, innervates several muscles in the anterior compartment of the leg, including the extensor hallucis longus.

Wait, but I should double-check. The anterior tibial artery is in the same compartment, so the nerve supply should be the deep peroneal nerve. The superficial peroneal nerve goes to the lateral compartment, which includes the peroneus longus and brevis. So the extensor hallucis longus is definitely supplied by the deep peroneal nerve.

Now, the options might have other nerves like the tibial nerve, common peroneal, or sciatic. The tibial nerve is part of the sciatic and supplies the posterior compartment. The common peroneal is the main branch but splits into superficial and deep. The deep peroneal is the one for the anterior muscles.

So the correct answer should be the deep peroneal nerve. Let me make sure there's no confusion with the superficial peroneal. The superficial peroneal nerve supplies the lateral compartment muscles, which are the peroneals. The anterior compartment muscles like tibialis anterior and extensor hallucis longus are from the deep peroneal. Yep, that seems right.

**Core Concept**
The extensor hallucis longus (EHL) is a muscle in the anterior compartment of the leg, responsible for extending the big toe. It is innervated by the **deep peroneal nerve** (also called the anterior tibial nerve), a branch of the common peroneal nerve. This nerve arises from the sciatic nerve (L4–L5, S1) and supplies motor function to anterior compartment muscles.

**Why the Correct Answer is Right**
The deep peroneal nerve innervates the EHL by supplying motor fibers to its proximal and distal parts. It also provides sensory innervation to the web space between the first and second toes. The nerve runs alongside the anterior tibial artery in the anterior compartment, passing through the interosseous membrane to reach the dorsal foot. Its role in EHL function is critical for dorsiflexion of the big toe, aiding in gait propulsion.

**Why Each Wrong Option is Incorrect**
**Option A:** *Superficial peroneal nerve* – Supplies lateral compartment muscles (peroneus longus and brevis); sensory to the lateral leg and dorsum of the foot.
**Option B:** *Tibial nerve* – Innervates posterior compartment muscles (e.g., gastrocnemius, soleus); sensory to the sole of the foot.
**Option C:** *Common peroneal nerve* – Divides into superficial and deep branches but does not directly supply the EHL.
**Option D:** *Sciatic nerve* – Parent nerve to the tibial and common peroneal nerves; does not directly inn

✓ Correct Answer: B. Deep peroneal nerve