To answer this question, you need to remember two things:
(1) slopes of parallel lines are identical and
(2) the slope of a second line perpendicular to the first is the negative reciprocal of the first line (e.g., if the slope of the first line is 2 then the slope of the second line is -1/2)
Now, rewrite the equation in question in slope-intercept form (y = mx + b):
11x - 6y = 21
11x - 11x - 6y = 21 - 11x
-6y = -11x + 21 (reorganizing)
-6y/-6 = -11x/-6 + 21/-6
y = 11/6x - 21/6
So, the slope of the line is 11/6
Then, any equation with the same slope (e.g., y = 11/6x) is parallel to it.
Finally, any line perpendicular will have a slope that's the negative reciprocal of 11/6 or -6/11.
So, one perpendicular line (out of many) would be y = -6/11x
Hope this helps!