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We need to find if |x|= y-z.

We know that |x| >=0. We also know that if x<0, |x| = -x.

With that in mind, lets look at the statements.

1. x+y = z
=> - x = y-z
Now if x<0, |x|= y-z
But if x>0, |x|= z-y

Insufficient.

2. x<0
We know nothing about y,z. Insufficient.

Together we know x<0, therefore -x =|x|, but from 1 we know that -x = y-z, hence |x| = y-z. sufficient

Hence C is correct.