we have
the slope of the given line is
[tex]m1=-6[/tex]
we know that
If two lines are parallel , then their slopes are the same
so
[tex]m1=m2[/tex]
if two lines are perpendicular, then the product of their slopes is equal to minus one
so
[tex]m1*m2=-1[/tex]
we will proceed to verify each case to determine the solution
case A) line m with slope [tex]6[/tex]
Compare the slope of the line m of the case A) with the slope of the given line
[tex]m1=-6[/tex] -----> slope given line
[tex]m2=6[/tex] ----> slope line m case A)
[tex]m1\neq m2[/tex]
[tex]m1*m2\neq-1[/tex]
therefore
the line m case A) and the given line are neither parallel nor perpendicular
case B) line n with slope [tex]-6[/tex]
Compare the slope of the line n of the case B) with the slope of the given line
[tex]m1=-6[/tex] -----> slope given line
[tex]m2=-6[/tex] ----> slope line n case B)
[tex]m1=m2[/tex] ------> the lines are parallel
case C) line p with slope [tex]\frac{1}{6} [/tex]
Compare the slope of the line p of the case C) with the slope of the given line
[tex]m1=-6[/tex] -----> slope given line
[tex]m2=\frac{1}{6}[/tex] ----> slope line p case C)
[tex]m1*m2=-6*\frac{1}{6}=-1[/tex] ------> the lines are perpendicular
case D) line q with slope [tex]-\frac{1}{6} [/tex]
Compare the slope of the line q of the case D) with the slope of the given line
[tex]m1=-6[/tex] -----> slope given line
[tex]m2=-\frac{1}{6}[/tex] ----> slope line q case D)
[tex]m1\neq m2[/tex]
[tex]m1*m2\neq-1[/tex]
therefore
the line q case D) and the given line are neither parallel nor perpendicular
the answer in the attached figure
