**Core Concept**
The question involves a patient with a spinal cord injury, specifically a transection of the right ventral primary ramus of L4. This injury affects the spinal nerves that arise from the thoracic and lumbar regions of the spinal cord, leading to potential motor and sensory deficits.

**Why the Correct Answer is Right**
The right ventral primary ramus of L4 gives rise to the L4 nerve root, which provides motor innervation to the iliopsoas muscle and sensory innervation to the skin of the thigh. Transection of this nerve root would result in weakness or paralysis of the iliopsoas muscle, leading to a positive Trendelenburg sign. The Trendelenburg sign is a clinical indicator of hip abductor weakness, where the pelvis drops on the opposite side of the injured limb when the patient stands on the injured limb.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not directly related to the injury described. The L4 nerve root primarily affects the thigh and hip region, not the lower back.
**Option B:** This option is incorrect because the L4 nerve root does not directly innervate the quadriceps muscle, which is responsible for knee extension.
**Option C:** This option is incorrect because the L4 nerve root does not directly innervate the gastrocnemius muscle, which is responsible for ankle flexion.
**Option D:** This option is incorrect because the L4 nerve root does not directly innervate the tibialis anterior muscle, which is responsible for ankle dorsiflexion.

**Clinical Pearl / High-Yield Fact**
The Trendelenburg sign is a useful clinical indicator of hip abductor weakness, which can be seen in patients with L4 nerve root injuries or other conditions affecting the hip abductors. It is essential to assess for this sign in patients with suspected hip or spinal cord injuries.

**Correct Answer:** D.