6 at third / 12 at fourth

If you mean:  (6^3) / (12^4)

This is [6 x 6 x 6] / [12 x 12x 12 x12]

  cancel the 6's into the 12's to get:  1 / [2 x 2 x 2 x 12]  =  1 / 96

Or, if you have to show all the exponential steps, 

Since  6 = 2·3,  6^3 = (2·3)^3  =  2^3 · 3^3

Since 12  =  4·3  =  2²·3,  12^4  =  (2²·3)^4  =  (2²)^4 · 3^4  =  2^8 · 3^4 

So:  (6^3) / (12^4)  =  [ 2^3 · 3^3 ] / [ 2^8 · 3^4 ]

                               =  1 / [ 2^5 ·  3 ]

                               =  1 / 96