Hi anonymous,  i am glad you voiced your opinion.  That helps spot errors and also helps learning.

Lets look at this

|14-15| = |-1| = 1    Because absolute value is the distance from 0 on the numberline so it is always positive.

|-11| = 11

and

1-11=-10

There are no absolute signs around this so the answer is -10

|14-15|-|-11|

=|-1|-+11

=1-11

=-10

If you want me to explain any of this better then just ask.  

i beg to diff.. it's not a negative ten but a positive ten 

Why wouldn't the |-11| be taken to RHS first? And the there is absolute value, then you cannot push the additional negative into the absoulte value right? So it drops away? Or else why are the absolute value signs there? I mean is this a trick question? If you take the -11 across first you'd have a different equation or isn't that possible? Why can't you put the additional negative into the absoulte value first? Thanks for clearing this up.

You cannot take anything to the right hand side because there is no right hand side.  This is NOT and equation,  it is just an expression. (I think that is the correct term)