Answer
$32\dfrac {rad}{s^{2}}$
Work Step by Step
Angular velocity of object is:
$w=\dfrac {\partial \theta }{\partial t}=\dfrac {\partial }{\partial t}\left( 2+4t^{2}+2t^{3}\right) =8t+6t^{2}............\left( 1\right) $
Angular acceleration of the object is:
$\alpha =\dfrac {\partial w\left( t\right) }{\partial t}...................\left( 2\right) $
Using (1) and (2) we get,
$\alpha =\dfrac {\partial w\left( t\right) }{\partial t}=\dfrac {\partial \left( 8t+6t^{2}\right) }{\partial t}=8+12t$
So, at time $t=2s$, we get:
$\alpha \left( 2\right) =8+12\times 2=32\dfrac {rad}{s^{2}}$
