Need help with hw question. I have answered but it is incorrect.Letter (b)

Given:
b)
[tex]y=2^{\frac{x}{3}}[/tex]The graph of the function is shifted to the right 6 units.
[tex]\begin{gathered} f(x)=f(x-6) \\ y=2^{\frac{x-6}{3}} \end{gathered}[/tex]The graph of the function is shifted to the down by 4 units.
[tex]\begin{gathered} f(x)=f(x)-4 \\ y=2^{\frac{x-6}{3}}-4 \end{gathered}[/tex]Answer:
[tex]y=2^{\frac{x-6}{3}}-4[/tex]