#### Answer

$48$

#### Work Step by Step

Formula to calculate the Flow is given by$ W=\int_C F(r(t)) \dfrac{dr}{dt}(dt)$
Here, $ \dfrac{dr}{dt}= i+2t j+0k$
Now, $\int_0^{2}(- 4t^3+8t^2 j+2k) (i+2t j+0 k)dt= \int_0^{2}(-4t^3)+(16t^3) dt$
Thus, $3[ (t)^4]_0^{2}=48$