The given function is
f(x) = |x|
Moving 4 units to right means, subtracting the number from x. So moving |x| 4 units to right will give:
f(x) = |x-4|
Moving 2 units up means addition of a number to the function. So moving 2 units up will give:
f(x) = |x-4| + 2
Thus, the correct answer to the question is option B