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Each set of six will start with the same number and just rearrange the other 3 numbers. This can be done with each number and therefore 6x4 is 24.
1234
1243
1324
1342
1432
1423
2134
2143
2314
2341
2412
2413
3124
3142
3214
3241
3412
3421
4123
4132
4213
4231
4312
4321
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