What Yash is saying is this:
The problem implies that there is plane common to the families of planes generated by the two sets of planes given
i.e. \exists \lambda, \mu such that (2x-2y+3z-2)+\lambda (x-y+z+1) \equiv (x+2y-z-3)+\mu(3x-y+2z-1)
The corresponding coefficients of x,y,z will be in proportion.