Answer
0.5 cm
Work Step by Step
The phase difference between beams that reflect from the top surface vs the bottom surface should be $180^{\circ}$ to produce destructive interference.
This occurs if the path difference between the beams is half a wavelength. The path difference is twice the thickness of the coating.
$$2t=\frac{1}{2}\lambda$$
$$t=\frac{1}{4}\lambda=\frac{1}{4}(2cm)=0.5cm$$