Answer
We can rank the four pairs according to the amplitude of their resultant wave:
$a = d \gt b = c$
Work Step by Step
We can find the amplitude of each resultant wave.
(a) The waves are out of phase by half a wavelength, so the interference is fully destructive.
The amplitude of the resultant wave is the difference of the two amplitudes.
$A = 6~mm-2~mm = 4~mm$
(b) The waves are out of phase by half a wavelength, so the interference is fully destructive.
The amplitude of the resultant wave is the difference of the two amplitudes.
$A = 5~mm-3~mm = 2~mm$
(c) The waves are out of phase by half a wavelength, so the interference is fully destructive.
The amplitude of the resultant wave is the difference of the two amplitudes.
$A = 9~mm-7~mm = 2~mm$
(d) The waves are in phase, so the interference is fully constructive.
The amplitude of the resultant wave is the sum of the two amplitudes.
$A = 2~mm+2~mm = 4~mm$
We can rank the four pairs according to the amplitude of their resultant wave:
$a = d \gt b = c$
