Amplitude is defined as the maximum distance from the rest position (equilibrium) to the crest (or trough) of a wave. In the case of a transverse wave, the amplitude can be determined by taking half of the vertical distance between the crest and the trough.
In your description, the distance from the top of a crest to the bottom of a trough is given as 4.2 centimeters. Therefore, to find the amplitude:
\[ \text{Amplitude} = \frac{\text{Distance from crest to trough}}{2} = \frac{4.2 \text{ cm}}{2} = 2.1 \text{ cm} \]
Thus, the amplitude of the wave is 2.1 cm.