In the step after -6x+10=4x+20, he moved the terms incorrectly. you have to add 6x to both sides so it would be 10=4x+6x+20 which simplifies to 10=10x+20. subtract 20 from both sides to get -10=10x. divide both sides by 10. the answer is x=-1
Take y=3 and plug it into y=-3x+6. This gives you 3=-3x+6. Solve for x, you get x=1. Now plug 1 into y=-3x+6 and you get 3. Answer is (1,3)