Step 1: Two-point discrimination measures the tactile acuity of a skin region. We ask: where is acuity worst, since that is where the two points must be moved farthest apart to feel like two?
Step 2: Acuity depends on the density of touch receptors and the size of their receptive fields. Densely innervated zones such as fingertips and lips have tiny receptive fields, so they resolve points only 2 to 3 mm apart.
Step 3: The skin over the back near the scapula is sparsely innervated with large overlapping receptive fields. Here two stimuli merge into one unless they are separated by roughly 65 mm, the largest separation among the choices given. So the answer is the back over the scapula.
Step 4: By elimination, lips, palm, and dorsum of hand are all high acuity sites with small thresholds and cannot be the region needing the greatest separation.
\[\boxed{\text{The back over the scapula}}\]