In order to determine the equation for the horizontal translation of y = |x|, take into account that translation to the right (just as you have in the graph) consists in subtracting a specific constant to variable x:
That is, a translation of u units is given by:
y = |x - u|
you can notice that the translation in the graph has been of 4 units, then, you have u = 4:
y = |x - 4| "this is the equation of the horizontal translation"