Discussion

Explanation:

It can be seen that every city is connected to all the other 3 cities.
If we start from city A, there are 3 ways in which we can proceed, viz. AB, AD or AC.
Once we are at any of these cities, each one of them is connected to the other 3 cities. But since we cannot go back to city A, there are only 2 ways in which we can proceed from here.
If we are at B, we can take either paths BD or BC.
From this point, we have a choice of going directly to A (thus skipping 4th city) or go to 4th city and come back to A. Eg. If we are at D, we can either take DA or DCA. So there are 2 more ways to go from here.
Hence, required number of ways = 3 x 2 x 2 = 12.

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