Question 1164489
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Since the 6 consonants are to be together, put them in a single group.  That gives us 4 items to be put in some order -- the 3 vowels, and the group of 6 consonants.<br>
Those 4 items can be arranged in 4! = 24 different ways.<br>
Within the group of 6 consonants, or which 2 are the same, the number of arrangements is 6!/2! = 720/2 = 360.<br>
The total number of arrangements with the 6 consonants together is then 24*360 = 8640.<br>