Since I'm doing my math homework anyway and this thread has been resuscitated, I guess I'll give you an in-depth explanation (although fsquared has given the best/easiest way).
Exclude the (-) sign because you know that it just flips the function over the x-axis.
Definition of absolute value:
|x|= x (if x≥0)
-x (if x<0)
So, in your problem,|x-4|is only non-negative if x is greater than or equal to 4. And it is negative if x is less than 4.
Therefore:
f(x) = x-4 if (x≥4)
-(x-4) if (x<4)
Now you have two linear functions that are easy to visualize and meet the x-axis at x=4.
Voila, it is clear that the graph moves to the right
. And I can't believe I just wrote all that, what has school done to me
?