How can the 13.8 billion years old universe have a radius of 46 billion light years? The universe is about 13.8 billion years old. Assume at the big-bang it starts from a small region and the maximum possible speed according Einstein is the speed of light how can the universe got a radius of 46 billion light years? According my understanding it could have a max. radius of 13.8 billion light years only. Can someone explain to a non-astrophysicists.
You assumption is wrong. Universe can( and is ) expand faster than the speed of light.

The photon emitted towards our planet in the early universe, had to traverse a universe that is expanding. That photon experienced redshift, that means his wavelenght increased and frequency decreased. We measure that photon's wavelength, compare it to a photon that was not redshifted and calculate the scale, which is then applied to the radius of the observable universe.

Reading this Wikipedia page should give you more complete understanding of the problem.

http://en.wikipedia.org/wiki/Observable_universe