The feasible region for the constraints $x-2 \leqslant y, x \geqslant y-1, x \geqslant 2, y \leqslant 4$, $x, y \geqslant 0$, is ...

Given the constraints $y \geq x-2$, $y \leq x+1$, $x \geq 2$, $y \leq 4$, $x \geq 0$, and $y \geq 0$, we analyze their geometric representations.

The inequalities $x \geq 0$ and $y \geq 0$ confine the region to the first quadrant, while $x \geq 2$ and $y \leq 4$ further restrict it to $x \geq 2$ and $0 \leq y \leq 4$.

The lower boundary lies on or above $y = x-2$, and the upper boundary on or below $y = x+1$.

Intersection points are found: $x=2$ with $y=x-2$ gives $(2,0)$; $x=2$ with $y=x+1$ gives $(2,3)$; $y=4$ with $y=x+1$ gives $(3,4)$; $y=4$ with $y=x-2$ gives $(6,4)$.

The feasible region is a quadrilateral with vertices at $(2,0)$, $(2,3)$, $(3,4)$, and $(6,4)$.

Option B matches this region, bounded by the lines corresponding to the constraints.