The clue says that the function f is a line with slope m and intercept b. Recall that the slope of line is change in y over change in x. Here, y is the same as f. Now look carefully at f(x+2) - f(x) = 6. It shows that when x increases by 2, the function f increases by 6. So the slope is 6/2 = 3.
We cannot determine the intercept from the given information, but it is not needed anyways. Whatever the intercept may be, the inverse function f-1 is a line perpendicular to f. Its slope is therefore -1/3. Again, remember that this is change in y (now f-1) over change in x. So if x increases by 3, then f-1 decreases by 1. The question however is how much does f-1 change when x increases by 2. The answer is a decrease by 2/3. That is, f-1(x+2) - f-1(x) = -2/3.
