Any plane passing through (3, 2, 4) is given by

where A, B and C are the direction ratios of the normal to the plane. Now, if this plane contains the x-axis, the normal to the plane must be perpendicular to the line (1st condition) and also the plane must pass through the origin (2nd condition).
Equation of x-axis is

1st condition gives

2nd condition gives

Putting in the equation of the plane, we get

This is the required equation.