The method is simple. The trick is pulling it off with SUBTLETY. Amazingly, most people do not know that dice are made such that the values on opposite sides always total 7 (if there's a 6 on one side, there will be a 1 on the other, etc.). So by catching a quick glimpse of the tops of the dice, you can figure out the values on the bottom.

You could look at each individual die and figure out what value is on the other side, or use a simple shortcut to get the total value on bottom: total up the values on the top of the dice, and subtract that amount from 21: your answer will be the secret number they're thinking of!