So you know the dot product? The dot product of 2 perpendicular vectors is 0.
So imagine you already have your plane. Now if you pick any point in your plane, call it (x,y,z), then the vector yo get from (x,y,z) - (2,-1,4) must lie on the plane right? or must be perpendicular to the z-axis. Then the vector (x-2, y--1, z-4) or (x-2,y+1,z-4), should be perpendicular to the z-axis, or the vector (0,0,1). so (x-2,y+1,z-4) * (0,0,1) = 0. which gives z-4 = 0, or z=4.