In 4 -> 5, he subtracted 3y from both sides. Then he subtracted 4x from both sides. Notice that the other side changed as well. In 5 -> 6, he factored by grouping. If you still don't get it after looking at the link I can explain it to you but I think it goes over the topic pretty well. In 6 -> 7, he divided both sides by (y-2) to get 2x = (-3y-1)/(y-2) and then divided both sides by 2 to get just x on the left side. The author made a slight mistake when he wrote [2(x-2)] when is should be [2(y-2)]. Were you trying to solve for x or find the inverse function?