I approached graphing $2^{4-x}$ by simplifying the function to $2^{-x}$ (i.e. the reflection in the y-axis of $2^{x}$), and then applying what I've learned that adding a constant to $x$ translates the graph to the left by $x$ units. My answer was wrong. The correct answer is $2^{-x}$ shifted to the right by 4 units.
I hope someone can provide a clear rule, or show how I should've thought about this properly. I figure it's because the coefficient on $x$ is negative that reverses the rule, but there's probably a cleaner way to think about it.