Question 878830
Think of each peg as a slot. There are 6 slots. For each slot, we have L (left) or R (right) to enter into it.


We have 2 choices per slot and 6 slots. So there are 2*2*2*2*2*2 = 2^6 = 64 different paths possible.


A probability tree would illustrate the idea, but drawing a tree with 6 different levels is very tedious and cumbersome.