Who are you paying for internet? You say your neighbor "charged you". Do you mean you don't pay the ISP anything? If so, then your neighbor is giving/selling you some of his internet. Not only is this against most ISP's ToS, but if you "hack it" you are taking speed away from your neighbor.
Since you don't seem to have a technical background, I am going to assume that diagram was drawn by your neighbor. If so, he has a better understanding of their network then you. Not only does this make it unlikely you will be able to "hack" his network, but doing so will make him aware, which will probably make him stop offering you internet what so ever. Don't look a gift horse in the mouth. Either use what your neighbor gives you or buy something better. Be thankful for what you have, it's Thanksgiving after all. XD