I read somewhere that the charge redistributes equally is if 20c is place on one end, both of the other ends of the parallel plate capacitor has +10c and -10c. I want to know why and how such redistribution occurs. Also, if such redistribution occurs isn't conservation of charges violated?
Suppose you have some series of parallel plates with charges $Q_1$, $Q_2$, up to $Q_n$, for example like this (I've drawn just four plates but this is going to apply to any number of plates):
Strictly speaking what I'm going to say only applies to infinitely large plates but in practice we just need the size of the plates to be large in comparison to their spacing. Anyhow, the charge on each plate distributes itself between the two faces of the plate in accordance with the rules:
the charges on the faces of a pair of plates is equal and opposite
the charges on the two outside faces are the same
if any plate is earthed the charges on the two outside faces are zero
If you're interested there is some discussion of why these rules apply in the question Why are the two outer charge densities on a system of parallel charged plates identical?
In your case you have just two plates, i.e. the two plates of your capacitor, and the charges are $Q_1 = 20C$ and $Q_2 = 0$. If we apply the rules above we find the charge distribution is:
Why would conservation of charge be violated in your example? A property of conductors is that, in electrostatic equilibrium there can be no field inside the conductor (for an ideal conductor, in real life there may be a small amount inside near the surface) and the conductor is at a constant potential. The excess change placed on a conductor is free to move about in the surface and any deviation from equilibrium will case changes to move until they find an equilibrium that satisfies the constraints previously mentioned.
What matters is that the total charge of all components in an isolated system remain fixed. The redistribution cannot change the total. In your example it would help if you provided some information on whether the caps are connected to each other or in isolation.