If AC = CD, then each is half of AD, so each has length 12/2 = 6.
If AB = BC, then each is half of AC, so each has length 6/2 = 3.
The lengths are:
... AB = 3
... AC = 6
... AD = 12
... BC = 3
... BD = 9
... CD = 6
Since we have just listed the lengths of "all segments in the diagram," we presume that is the list from which our random segment is chosen. Of these 6 segments listed, 4 are longer than 3. The probability of interest is ...
... 4/6 = 2/3
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If you consider the segments in the diagram to be only AB, BC, and CD, then your probability is 1/3, since only CD is longer than 3.
