Find the Flux of the Curl of Field F Through $\theta$

Multiple Choice

Find the flux of the curl of field F through the shell S.
-F = 6yi - 6zj + 4xk; S: r(r, $\theta$ ) = r cos $\theta$ i + r sin $\theta$ j + ( 4 - ) k, 0 $\le$ r $\le$ 2 and 0 $\le$ $\theta$ $\le$ 2 $\pi$

A) - 24 $\pi$
B) -12 $\pi$
C) 24 $\pi$
D) -24