Multiplication property of Equality. I tried my best to decipher the text you added, and it seems to me like you end up multiplying both sides of the equation by 8/3. This is the reciprocal of 3/8, so multiplying them together leaves you with -x. When 48 is multiplied by 8/3 you get 128, so x=-128. The Multiplication Property of Equality states that if you multiply both sides of an equation by the same number, the sides remain equal.
You take 64 miles for 2 gallons and divide it by 2. And it leads up to 32 miles and 1 gallon. Now you divide that by 2 again and get 16 miles and 1/2 gallon. So, to check that you can take 16+16 and you get 32 and take 32+32 and you get 64.
