As kuruman says, it's helpful to provide links to things you want to ask questions about. We're helping out just for fun, and you're more likely to get help if we only have to click on one link rather than hunt through search engines for references. It isn't always possible to provide links, of course, but the Feynman Lectures are all online on CalTech's website -
this is chapter 6.
He's proposing a game: toss a coin and if you get heads take a step to the left, if you get tails take a step to the right. If you keep repeating this game, how far will you be from your starting point? The answer is the difference between the number of heads you've got so far and the number of tails you've got so far. This is ##D##. He does algebra to get different expressions for ##D## in terms of the total number of tosses and the number of heads. This is useful because ##N## is not a random number and nor is 2, so the randomness of ##D## is dictated by the randomness of ##N_H##, and he already did the maths for that.
6.11 is just a rearrangement of ##D=2N_H-N##, stated in the paragraph above. 6.12 expects you to use 6.11 to see that the left hand side is the same as half the rms value of ##D## and then 6.10 to get the right hand side.
If that doesn't make sense, say which bits you don't follow and we'll see what we can do.