In the first orientation L and S are parallel and pointin in opposite directions. In this case J has to be minimal with J = |L-S| = |1 – 1 | = 0.
In the second orientation J = | 1 – 0 | = | 0 – 1 | = 1
The orientation parallel and pointing in the same direction corresponds to J = | 1 + 1 | = 2