Since the three people want to follow each other treat that group of three as one person. But first determine how many combinations those three people can take.
If they are called A, B and C the first person could be any of the three 3, while the second person could be any of the remaining 2, and the third person is the remaining one. So amongst those three people there are 3*2*1 = 6 possible orders.
With that group taken as one unit (call ABC G, the group), there are 4 choices for the first spot (G, D, E, F) 4, and then 3 choices for the second spot, 2 for the third and 1 for the final spot. So that's 4*3*2*1 = 24 possibilities.
The total is 6 * 24 = 144 possible combinations.
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