X- (1/6)= (1/12)
Add (1/6) to each side
x = (1/12)+(1/6)
x=(1/12)+(2/12)
x=(3/12)
x=(1/4) or .25
For the limit approaching 3 from the right, you want to follow the line to the right of x = 3. From the graph you're describing it sounds like that's y = -3.

The RHS limit is -3 even though f(3) = 7
If you would like to divide 2/3 by 1/2, you can do this using the following step:
2/3 / 1/2 = 2/3 * 2/1 = 4/3 = 1 1/3
The correct result would be 1 1/3.