In which of these cases are the two wave points considered to be in phase with each other?

a.
one point is on a crest and the other point is on a trough.
b.
one point is at the equilibrium position and the other point is on a trough.
c.
one point is at the equilibrium position and the other point is on a crest.
d.
the two points are both on troughs.

D.  

The two points are both on troughs.

Explanation:

If two points are in phase then the distance between the two points must be equal to the wavelength.

As we know that distance between two trough or two crest is always in the multiples of wavelength so here if we take two points on either of two crest or on two trough then the two points must be in same phase or the phase difference between the points must be zero

so here correct answer would be

D.  

The two points are both on troughs.