Start off with differentiating x = b + 2b cos (nt) with respect to time until you get to acceleration. Then put acceleration in the form -n^2(x-c) to assist with substitution.
From the question, when:
x = 3b, |\ddot{x}| = 16
and
x = 2b, |\dot{x}| = 4\sqrt3
Substitute the conditions into the...