Answer
$-16 \pi$
Work Step by Step
Green Theorem, Tangential form for Counterclockwise Circulation, can be defined as:
$\oint_C F \cdot T ds= \iint_{R} (\dfrac{\partial N}{\partial x}-\dfrac{\partial M}{\partial y}) \space dx \space dy $
Now, $$\oint_C F \cdot n ds= \iint_{R} \dfrac{\partial (y+2x)}{\partial x}-\dfrac{\partial (6y+x)}{\partial y} \space dx dy \\= -4 \iint_{R} dx dy
\\= -4 \times Area \space of \space circle \space with \space radius \space 2 \\= -4 \times \pi \times (2)^2 \\=-16 \pi$$
