I was going over homework problems and had a question where the transformations 2f(3(-x+2))-4 were applied to f(x) = √x
For the √x point (0,0), that answer I got after the transformations was (-2, -4), as I thought I needed a horizontal translation 2 left. However, the answer sheet says it should be (2, -4)
Does this mean that the -x causes the translation to be reversed, or have I made a mistake?
It is not simply a matter of the translation being rightward instead of leftward. The fact that it is $-x$ instead of $x$ causes the entire graph to be mirror-imaged.
There are various ways to get the end result. One is to mirror-image the graph around the $y$ axis and then translate $2$ units to the right. Another is to translate left and then mirror-image the graph. If you allow reflections around other lines you have even more ways to get the result.
For the particular case of the image of $(0,0),$ consider when it will be true that $3(-x+2) = 0$.