Which of the following equations best describes the graph given below?

In these type of questions
we go through the options :
Now when x=6 or -6 the value of y is 0
so let us put value of y=0 in all options and check which option satisfies x=6 and -6
Putting x=6 and y=0 in option A
we get |6+0|-|6-0| = 0
But RHS =6 so this option is discarded
Now putting in option B
|6-0|+|6+0| =12
But RHS is 10
so this option is also discarded .
Now option C we get
|6|-0 =6
so we can say graph can be of |x|-|y|=6
Now satisfying option D
we get |6+0|-|6-0|=0
So we can say 6,0 and -6,0 satisfies option D as well
Now you have to eliminate between C and D
If you observe |x+y|-|x-y|=0 will pass through origin
and the graph here is not passing through origin so you can eliminate option D
Therefore the graph will be |x|-|y|=6