How does the photoelectric effect support …

The photoelectric effect supports a particle theory of light in that it behaves like an elastic collision (one that conserves mechanical energy) between two particles, the photon of light and the electron of the metal.

If you shine light on a metal of any intensity with energy below the binding energy of an electron, no electrons from the metal will be ejected. As soon as the frequency of light is high enough such that the energy exceeds the binding energy, the electron from the metal can be knocked off the metal.

If the energy of the photon that hits the metal is hν, then energy will be conserved in the collision so that

hν=BE+KEelectron

The energy before the collision is hν. The minimum amount of energy needed to eject the electron is the binding energy, BE. However much hν exceeds the binding energy will be the kinetic energy KE of the ejected electron.

Conservation of energy in collisions is particle like behavior and thus the photoelectric effect supports light's particle like behavior.