Accelleration is the second derivative of the position function, or the first derivative of the velocity function.
You already found s'(t) = v(t) = 8cos(4t) + c
To find c, plug in t=4 and v(t) = -7.6.
Then, take the derivative of the velocity equation. That will give you your acceleration function. Then plug in t = 4 into the acceleration function.
Edit: Sorry about the double post... I was too slow I guess.