First, let's simplify the expression step by step.

-54 a^6 b^(9/12) (-c^(20/12) / (12 a^4 * b^15))

-54 a^6 b^(3/4) (-c^(5/3) / (12 a^4 * b^15))

Now, let's simplify the expression further:

-54a^6 b^(3/4) -c^(5/3) / (12 a^4 b^15)

(54 a^6 b^(3/4) c^(5/3)) / (12 a^4 * b^15)

54/12 simplifies to 9 and a^6 / a^4 simplifies to a^2:

9 a^2 b^(3/4) * c^(5/3) / b^15

Now, let's simplify further:

9 a^2 b^(3/4 - 15) * c^(5/3)

9 a^2 b^(-57/4) * c^(5/3)

So, the simplified expression is:

9a^2 b^(-57/4) c^(5/3)