The vertical displacement of the wave is measured from the ?
equilibrium to the crest and is called the frequency.
crest to the trough and is called the amplitude.
trough to the trough and is called the wavelength.
equilibrium to the crest and is called the amplitude.

The whole question is talking about the amplitude of a wave
that's transverse and wiggling vertically.

Equilibrium to the crest . . . that's the amplitude.

Crest to trough . . . that's double the amplitude.

Trough to trough . . . How did that get in here ?  Yes, that's
                               the wavelength, but it has nothing to do
                               with vertical displacement.

Frequency . . . that's how many complete waves pass a mark
                       on the ground every second.  Doesn't belong here.

Notice that this has to be a transverse wave.  If it's a longitudinal wave,
like sound or a slinky, then it may not have any displacement at all
across the direction it's moving.

It also has to be a vertically 'polarized' wave.  If it's wiggling across
the direction it's traveling BUT it's wiggling side-to-side, then it has
no vertical displacement.  It still has an amplitude, but the amplitude
is all horizontal.