A and J represent the gracile fasciculus, while B and I represent the cuneate fasciculus. Together they make up the dorsal column-medial lemniscal tract, responsible for pinpoint perception, proprioception, vibration, and pressure. Input is ipsilateral.
C and H make up the lateral corticospinal tract (also called the lateral cerebrospinal fasciculus), responsible for motor command of ipsilateral limbs.
D and G represent the lateral spinothalamic tract. It is responsible for pain and temperature conduction. The input arises in a limb (left lower extremity in this case), enters through the dorsal root (pictured between J and H), decussates and ascends at the anterior commissure (just behind E and F), and finally synapses on the second order neuron in the lateral spinothalamic tract. So the spinothalamic tract is responsible for contralateral pain and temperature sensation. Because our patient has lost sensation on the left, the lesion is in the right.
E and F are the anterior corticospinal tract. It is involved in motor control of proximal muscles, typically of the trunk.