Mark a particular face X. (Later on, we will have to divide whatever answer we get by 6 because all 6 faces are identical at this point, and we have chosen one out of 6 randomly).

Put a colour on face X. There are 6 ways to do this.

Put another colour on the face opposite X. There are 5 ways to do this.

Arrange the remaining 4 colours in the remaining four places - there are 3! ways to do this (circular permutation of 4 colours = (4-1)!

Total = $\frac{\left[\right(6\times 5\times 3!\left)\right]}{6}$ = 30