A
transverse wave is found to have a distance of 9 cm from a trough to
a crest, a frequency of 12 Hz, and a distance of 9 cm from a crest to
the nearest trough. Determine the amplitude, period, and wavelength
of such a wave.

The amplitude is HALF the distance from trough to crest (although saying it like that is a little confusing)...if you're talking about a transverse wave, then this distance is perpendicular to the direction the wave is traveling.

So the amplitude is 9/2 = 4.5cm

In terms of information, the period is essentially the same as the frequency (in fact the period is just 1/ʋ):

= 1/(12 Hz) = 1/12 seconds

Wavelength = 2*9 = 18 cmPlease select my answer as the best if it was helpful to you. Thanks