The plot of the absolute value function y=|x| looks like a ∨ with the vertex at the origin and the sides having slope -1 or 1. Your function
f(x) = 6|x|
is a vertically scaled version of that. The scale factor is positive and there is no translation, so the vertex will still be at the origin. The scale factor of 6 means the sides of the ∨ will have a slope of -6 or +6.
The appropriate choice is C.