Write an equation of the cosine function with amplitude 3 and period 4π.

Y = 3cos(x/2)

Let your cosine function be y = acos(cx)
Amplitude: a
Period: 2π/c

If we want to write an equation with an amplitude of 3, we'd just change the a to a 3:
y = 3cos(cx)

Now, since our normal cosine function has a period of 2π, we can manipulate the inside to have an period of 4π. 
2π/c = 4π
c = 2π/4π = 1/2
So, we'd just change c to 1/2 to get our final function:

y = 3cos(x/2)