Classic integral calculus.

The starting point to you question is given as acceleration. The integral of acceleration is velocity, and the integral of velocity is displacement. Conversely, if you were to go the other direction (differential calculus), velocity would be the derivative of displacement and acceleration would be the derivative of velocity. Simple Newtonian mechanics.

In math language:

Acceleration is constant = a
Velocity = a(t)+vo
Displacement = [a(t)^2] /2 + v(t) + do

Plug in the numbers. You guys have already solved the velocity question correctly, but no one has given the right displacement answer yet.

v(t) = 2 m/s (6 sec) + 0, (Plus zero because the object started from rest) = 12 m/s.

The displacement has to be solved in two parts, because the object is undergoing acceleration for the first 6 seconds, and travels at constant velocity for the remaining 8 seconds.

d1(v=0m/s,d=0m) = [2m/s^2(6 sec)^2] /2 + 0 m/s(6 sec) + 0 ft = 36 m

d2(a=0m/s^2, v=12m/s, d=36m) = [0m/s^2(8 sec)^2] /2 + 12 m/s(8 sec) + 36 m = 132 m.

An answer is only of value when accompanied by an explanation. Good day, gentlemen.