Your third line is wrong. Your fourth line is actually g(f(x)), not f(g(x))! Your fifth line has an extraneous x.
The important thing here is to realize that f(something) means that you replace x in the definition of f with "something". So here, f(3x+1) means you replace x in 1-4x with f(x) = (3x+1), resulting in f(3x+1) = 1-4(3x+1). Do you see that?
Yes.So would it then be rewritten as: 1-4(3x+1) ?