The easiest, and probably most illuminating, method is to look at the diagram above. Nevertheless, I thought I would give an explicit example.

\$$S=\\{1,2,3,4\\},\,\,T=\\{12,3,4\\}\$$.

c=[124][3], d=[1234], e=[12][3][4]

\$$g^* (\mathrm{d})\$$=[1234], \$$g^* (\mathrm{e})\$$=[12][3][4]

[124][3]\$$\leq\$$[1234] and [124][3]\$$\nleq\$$[12][3][4].