Answer
$$3$$
Work Step by Step
The work done by a force $F$ in moving a particle along path $C$ can be defined as: $ \iint_{C} F \cdot dr $
Stokes' Theorem states that $\iint_{S} curl F \cdot dS=\int_{C} F \cdot dr $
Consider$S$ to be the part inside the rectangle formed by four points.
Now, we have: $curl F=8 yi+2 z j+2y k$
and $$\iint_{S} curl F \cdot dS=\iint_{D} 2y-z dA \\=\dfrac{3}{2} \iint_{D}y dA \\=\dfrac{3}{2} \times \int_{0}^1 \int_0^2 y dy dx\\ =\dfrac{3}{2} \times \int_{0}^{1} [\dfrac{y^2}{2}]_0^2 dx \\=\dfrac{3}{2}] \times \int_0^1 2 dx\\=3$$
