I can't figure out 6 - 2/3r = 1 1/2

The way we're learning how to solve it, is by using the LCD. the LCD I use is 6
The book says the answer is 6 3/4
But I keep getting the wrong answer.

6 - 2/3r = 1 1/2

-2/3r = 1 1/2 - 6
-4/6r = -4 3/6
r = -4 3/6 divided by -4/6
r = -27/6 * -6/4
r = 162/24 = 6 3/4