((2x^3)^4 - (x^2)^6) : (3x^12)=

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To simplify this expression, we need to expand and simplify each term first:

(2x^3)^4 = 2^4 x^(34) = 16x^12
(x^2)^6 = x^(2*6) = x^12

Now we can substitute these values back into the expression:

(16x^12 - x^12) / (3x^12) = 15x^12 / 3x^12 = 5

Therefore, the simplified expression is 5.