You transformed the function as follows:
[tex]f(x)\mapsto f(x-6)[/tex]
All trasformations of the fashion [tex]f(x)\mapsto f(x+k)[/tex] translate the function horizontally, k units right if k is positive, k units left if k is negative.
In your case, k=6, so you translated the original function y=|x| 6 units to the right.
