Answer:
f(x) = |x - 12| - 10
Explanation:
Start with the "parent" function f(x) = |x|.
To shift down 10 units, subtract 10 from the function's formula.
|x| - 10.
To shift the graph right 12 units, replace x with x - 12.
g(x) = |x - 12| - 10.
Horizontal shifts often look they're being done backwards. A shift to the right 12 units calls for replacing x with x - 12 (minus!). The reason is that if you're graphing the function g(x) and you pick some value for x, say 8, you have to go back (left) 12 units to see what value f has in order to "copy" it to g.
g(8) = f(-4)