Can two wavefronts cross each other?

Hint: A wavefront is the locus of points characterized by the propagation of position of the same phase. A wavefront is a surface in which an optical wave has a constant phase. The direction of the wave is perpendicular to the surface of the wavefront at every point

Complete step by step solution:
A wavefront is described as the continuous locus of every particle and vibrating in the same phase. The perpendicular line drawn at any point on the wavefront denotes the direction of propagation of the wave and is called the ‘ray’.
 The wavefronts can be of different shapes. In general, we experience three types of wavefronts they are spherical wavefront, cylindrical wavefront, plane wavefront
Wavefront, imaginary surface denotes corresponding points of a wave that vibrate in unison. When identical waves having the same origin passes through a homogeneous medium, the corresponding crests and troughs at any instant are in a phase that is they have finished similar fractions of their cyclic motion, and any surface mark through all the points of the same phase will bring a wavefront
Finally, the wavefronts cannot cross each other because all rays take the same time to go from one wavefront to other
Finally, the answer is No, the two wavefronts do not intersect each other. when the wavefronts intersect then there will be two directions of propagation of the energy at the point of intersection of the wavefronts. That is not possible.

Note:
A surface of a constant phase is known as a wavefront.
Always a wavefront is normal to the light rays.
A wavefront does not travel in the backward direction.