So we want to know how long should we make the simple pendulum so it's period is T=200 ms = 0.2 s. Since the formula for simple pendulum is T=2*pi*sqrt(L/g) where T is the period, L is the length and g=9.81 m/s^2. Now we need to invert the formula to get the length: T/2pi=sqrt(L/g), we square both sides of the equation: (T/2pi)^2=L/g and multiply both sides with g: g*(T/2pi)^2=L. Now we input the numbers and get that the length L= 0.00995m.
