Numerical Methods: Euler to Runge–Kutta · Hard problem

The classical RK4 method (global error $\approx Ch^4$) is run on $0 \le t \le 4$ with step $h = 0.2$, and the error at $t = 4$ is $1.6 \times 10^{-3}$. The error must be brought down to $1.6 \times 10^{-7}$ using equal steps. What is the smallest number of steps across $[0, 4]$ that achieves this?