Answer
$0$
Work Step by Step
Applying Stoke's Theorem, we have
$\oint F \cdot dr=\iint _S (\nabla \times F) \cdot n d\sigma$
Here, $(\nabla \times F)=8yi$ and $n=\dfrac{1}{\sqrt 2}j+\dfrac{1}{\sqrt 2}k$
This implies that $(\nabla \times F) \cdot n=0$
Then, we have
$\iint _S (\nabla \times F) \cdot n d\sigma=\iint _{R} (0) d\sigma $
This implies that
$\iint _S (\nabla \times F) \cdot n d\sigma=0$