When y > 1/2,
|y - 1/2| = (y - 1/2)
and the inequality becomes
(y - 1/2) > 11/2
y > 6
OR
When y < 1/2,
|y - 1/2| = -(y - 1/2)
and the inequality becomes
-(y - 1/2) > 11/2
y - 1/2 < -11/2
y < - 5

Among the options, A, B, D, E satisfy the inequality. Only C does not.
You get the same by plugging-in the options into the given inequality.

You've either missed out a 'not' in the problem or the sign of the inequality should be '<' instead of '>'