Assume frequency response of x(t) is X(f). Find frequency response of x(-2t+4)?
The key is to apply 'shift and scale'. So for $x(-2t + 4)$, you would first do $x_1(t) = x(t+4)$, then $x_2(t) = x_1(-2t) = x(-2t + 4)$. 

So $X_1(f) = e^{-j2\pi f(-4)}X(f)$ = $e^{j8\pi f}X(f)$. 

Then $X_2(f) = \frac{1}{|-2|}X_1(f/-2)$ = $\frac{1}{2}e^{j-4\pi f}X(f/-2)$

In your answer how did you assume it is symmetric? Also, in your third step, for $x(-t)$, you should be getting $x(2(-t-2)$ instead of $x(-2(t-2))$. Your first 2 steps were correct but failed to use scaling factor -2 instead of 2 in the first step itself.