I believe your integral is wrong.

Also, as you were told, the maximum velocity occurs when a = 0.

0 = 12 - 6t

t = 2 s

Then, we come to the velocity function.

v = \int 12 - 6t dt

v = 12t - (6t^2)/2 dt

v = 12t - 3t^2

From there, can you work out the maximum velocity?

Displacement involves yet another integral, but this time:

s = \int 12t - 3t^2 dt

Find the value of s when t = 4.

Post what you get!