The slope of a line can be identified with the equation of the line as the number that is being multiplied by the variable x, then for the given equation y = 3x -6 the slope is 3 and for the second equation y = -3x + 9, then the slope of the second line equals -3.
For a pair of lines to be parallel their slopes must be the same, as you can see the slope of the first line is 3 and the slope of the second line is -3, then these lines are not parallel.
For a pair of lines to be perpendicular the product of their slope must be equal to -1, this means that if you multiply the slope of the first line by the slope of the second line and you get -1, then the lines are perpendicular, by multiplying 3 (slope of line 1) by -3 (slope of line 2), we get -9, since we didn't get -1 these lines are not perpendicular.
Then, the lines are neither perpendicular nor parallel, the last option, neither, is the correct answer.