Multiplying f(x) by 6 creates a vertical stretch of factor 6. To reflect across the y-axis we replace x with (-x).

Thus g(x)=6(4(-x))=24(-x)=-24x.

g(x)=-24x

The graph of f(x) (red), 6f(x) in blue(vertical stretch) and g(x) (reflection over y-axis) (green):