The number of different words that can be formed using all the letters of the word “SHASHANK” such that in any word the vowels are separated by at least two consonants is 

The letters other then vowels are SHSHNK which can be arranged in   $\frac{6!}{2!2!}$
Now in each case, let the first A be placed in the r^th gap then the number of ways to place the 2^nd A will be $(7-r-1), 1\le r\le 5$
So the total number of ways =   $\frac{6!}{2!2!}\underset{r=1}{\overset{5}{ }}(6-r)$
$=\frac{6!}{2!2!}\times (5+4+3+2+1) = 2700$