The slope of ef is -3/2 which segments are perpendicular to ef choose all that are correct

To answer this adequately, you'll need to find the slope of each of the four given line segments.  I note that the slope of the fourth one, NP, is

        -6 + 3        -3
m = =
          2 - 0         2

This slope is the same as that of the given line, and therefore these 2 lines are parallel, not perpendicular.  So eliminate the fourth possibility and concentrate on the other 3 until you find the one that has slope +2/3.  Reminder:  perpendicular lines are characterized by negative reciprocal slopes.