**Core Concept**
The question requires knowledge of the anatomy of the lower limb arteries, specifically their location and accessibility for palpation. The arteries of the lower limb arise from the aorta and branch into smaller vessels, some of which are more superficial and easily palpable than others.

**Why the Correct Answer is Right**
The **Posterior Tibial Artery** is challenging to palpate due to its deep location within the leg. It arises from the popliteal artery, passes behind the medial malleolus, and continues down the posterior aspect of the tibia. The posterior tibial artery is responsible for supplying blood to the muscles and bones of the posterior leg and foot. Its deep location makes it less accessible for palpation compared to other arteries in the lower limb.

**Why Each Wrong Option is Incorrect**
**Option A:** The **Femoral Artery** is actually one of the easier arteries to palpate in the lower limb, as it is located superficially in the femoral triangle.

**Option B:** The **Popliteal Artery** can be palpated at the popliteal fossa, although it may be more challenging due to its location behind the knee.

**Option C:** The **Dorsalis Pedis Artery** is actually one of the more easily palpable arteries in the lower limb, as it is located on the dorsum of the foot.

**Clinical Pearl / High-Yield Fact**
When assessing peripheral pulses, it's essential to remember that the presence or absence of a pulse does not necessarily indicate the presence or absence of arterial disease. A thorough examination of the lower limb should include assessment of capillary refill, temperature, and skin integrity.

**Correct Answer:** C. Dorsalis Pedis Artery