Need cuz i really don't know which of the following expressions is equal to 0 for some value of x?

The key is the absolute value is always positive or zero.  So when we add one to it we'll necessarily be positive, no chance of zero.  So the only one that has a chance is A, with the subtraction outside the absolute value. 

When x=0 or x=2 we'll get

|x-1| - 1 = 0