Question

Why western ghats are covered by thick forests and not eastern ghats?

Answer 1

Because many rivers fall in western ghats...they made a slope and form small delta..which provide a ideal environment for growth of forests

Answer 2

So these south west trade winds evidently enter India from the south west, and then gets bifurcated. So, if you see, the BoB branch travels directly to the north east and then brings rains there. The eastern ghats do receive some rain, but not as much as the western ghats, which receive the major part of the Arabian sea branch.
In simpler words, the western ghats receive more rainfall than the eastern ghats and therefore there is more vegetation cover as rainfall is directly proportional to the vegetation cover. More rainfall leads to more vegetation and therefore western ghats are covered with thick forests and not the eastern ghats as the eastern ghats do not receive as much rainfall to support the amount of vegetation present in the western ghats.