Dark matter is electrically neutral I would like to know how come if dark matter was electrically charged it would reflect light. What are the equations or the logic behind it? 
 A: How do you know something is electrically charged? Well, it interacts with other charges. Classically, this is described by the Maxwell equations, i.e. by fields. One special case of such an electromagnetical field, the plane wave, is what we call light (amongst other phenomena, radio transmission etc.).
That's pretty much it!

Perhaps it's actually easier understand from a more "modern" point of view: in QFT, the electromagnetical fields are quantised to particles called photons. In "slow" processes like electrostatic repulsion of balloons, those photons have low frequency, and thus tiny energy $E=\hslash\cdot \omega$, where $\hslash$ is the minute (by classical measures) Planck quantum. Therefore, we recognise the interactions readily as smooth fields.
At higher frequencies, such as light ($\approx 10^{18}\:\mathrm{Hz}$), the energy for each quantum is much higher, so when an atom emits light it's much more naturally single photons we're dealing with. But in principle, both are the same thing.
A: In order for something to interact with light, it must be electrically charged. All the things around us that reflect light (or otherwise interact with it) are charged.
Yes, the mirror (for example) is electrically neutral, but the light is interacting with the electrons on the surface - in a crude way, at least.
The question works flipped around as well - "why can't we see dark matter?" Not seeing means it doesn't emit light; how is light created? By the acceleration of charged particles. Thus, dark matter must be electrically neutral.
A: 
I would like to know how come if dark matter was electrically charged it would reflect light. What are the equations or the logic behind it?

The equations are the Maxwell equations and the quantum electrodynamics ones when photons ( which are the constituents of reflected light) interact with matter.  Note: matter as we know it consists of neutral atoms/molecules which are bound states of electrons and protons, charged ions and electrons.
If the energy of the photons is low they will scatter/reflect from the electrons in neutral matter and thus matter will be detected. More so if there exists a plasma which by itself also radiates photons and is detectable.  If the photons  are high energy they can interact with the nucleus of the atoms/molecules. Matter in bulk always emits photons that follow the black body radiation curve. If hot enough as in stars, the photons are in our visible light range. Photons are how we know of the existence of the universe around us.
Dark matter was posited in astronomical observations to explain/balance the rotations of galaxies  with Newton's equations of motion. There seemed to be mass missing:
The astronomers calculate/estimate  the mass of the galaxies from the light they emit using the physics we know and have tested in the lab. One can also estimate the mass of the galaxies from their rotational curves. The measurements can be brought to agreement, luminosity and gravitational ,by  assuming that part of the matter in the galaxy does not contribute to the luminosity, i.e. emit any electromagnetic light in the form expected by the equations that define how matter interacts electromagnetically, assuming   the thermodynamic balance  of the galaxy as it emits light.
Thus "dark matter" was brought forth as a hypothesis and is the standard accepted explanation one as far as I know.
