SOLUTION: How many words consisting of four consonants and 2 vowels can be formed?

First we calculate how the arrangement will be made.
For example CCVCCV or CVVCCC, etc. 

There are 6C2 places to choose to put vowels.
That leaves 4C4 = 1 way to put consonants. 

For each of those we can choose and position 4 
consonants 21P4 ways.
For each of those we can choose and position 2 
vowels 5P2 ways.

Answer: 

(6C2)(4C4)(21P4)(5P2) = (12)(1)(143640)(20) = 34473600

Edwin