i have been given this question: v(t)=3t^2-6t and i have to find when the object it is at rest?

Miss Melody should this be 3t(t-2)

Then t=0 and t=2

The object is at rest when velocity = 0

$$\\0=3t^2-6t\\\\
0=3t(t-6)$$

the object is at rest initially and at rest again after exactly 6 units of time :)

Thanks Lance, you are right of course :))