Answer
$128\dfrac {rad}{s}$
Work Step by Step
Angular velocity of object is :
$ω=\dfrac {\partial \theta }{\partial t}=\dfrac {\partial }{\partial t}\left( 2+4t^{2}+2t^{3}\right) =8t+6t^{2}$
So, when $t=4s$:
$ω\left( 4\right) =8t+6t^{2}=8\times 4+6\times 4^{2}=128\dfrac {rad}{s}$
