Don't be fooled by the seemly complexity of this question.
The question asks if a=|b|. With absolute value questions your first relection should be "do we know it's sign?" |b| is non negative. If we aren't able to determine if a is non negative then we can't determine if a=|b|.
Now look at the stem: a^2-b^2=b^2-c^2
and the two choices:
b=|c| and b=|a|
All we know is b is non negative. Do we know anything about a's sign? No!
Honghu, I am not sure if your approach to this particular question is right, because the question is really asking us whether a = b irrespective of their signs, so this can be deduced to is a^2 = b^2.
the question isn't asking whether a=b irrespective of their signs...
it asks for whether a = |b|
which would mean that a can't be negative
if signs didn't matter the question would be is |a|=|b|