Two ideas decide this: plasticity and crossing.
Phantom limb pain is the classic example of maladaptive cortical reorganisation. When a limb is amputated, its patch on the primary somatosensory map is suddenly starved of input. Cortex hates silent territory, so the AFFERENT fibres of the neighbouring representations (face, residual stump, etc.) sprout sideways and OVERLAP onto the orphaned limb area. Now, touching the face activates the limb's old cortical zone, and the brain interprets it as coming from the limb that is no longer there - felt as phantom sensation or pain.
Now place it in the correct hemisphere.
The somatosensory system is crossed (decussated): each half of the body is mapped on the OPPOSITE cerebral hemisphere. A RIGHT-sided amputation therefore deafferents the limb zone in the LEFT somatosensory cortex, and it is into that LEFT-hemisphere zone that the adjacent fibres project and overlap.
Filter the options.
$\bullet$ The mechanism must be "projection/overlap of adjacent fibres," not "expansion" of the limb's own cortex - so the expansion options (C, D) describe the wrong process (the deprived area is invaded/shrinks, it does not expand).
$\bullet$ It must be the LEFT cortex for a RIGHT limb because of contralateral wiring - so the right-cortex options (A, C) are wrong-sided.
The only choice that gets BOTH the mechanism (adjacent-fibre overlap) and the side (left cortex) right is B. This is also why therapies such as mirror-box training help: they feed corrected visual input to the reorganised left-hemisphere zone and partly reverse the maladaptive remapping that drives the phantom pain.