Prakhar has six biased coins with him; whenever he tosses any four coins, the probability of him getting at least one head and at least one tail is equal to 1. How many coins with Prakhar have only either heads or tails on both sides?

Let's say Prakhar has only one coin with heads on both sides. If there is only one such coin, then there would be cases in which he chooses 4 out of those six coins, but he does not pick that coin 
Then, his probability of getting at least one head can not be 1. 

For this probability to be 1, he must have at least three coins with heads on both sides. So, no matter what four coins he picks, he picks one coin with heads on both sides, resulting in his probability of getting at least one head 1. 

The same logic applies to tails; he must have three coils with tails on both sides. 

Therefore, all six coins with prakhar have either heads or tails on both sides. 

Hence, Option E is the correct answer.