3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b

3abc^4/12a^3(b^3c^2)^2 * 8ab^-4c/4a^2b

Expand term 1:
3abc^4/12a^3(b^3c^2)^2
3abc^4/12a^3b^6c^4

Now simplify term 1:
3/12 = 1/4
c^4 terms cancel
Subtract powers from variables since the denominator powers are higher:
b^(6 - 1) = b^5
a^(3 - 1) = a^2
1/4a^2b^5

Now simplify term 2:
8ab^-4c/4a^2b
8/4 = 2
2c/a^(2 - 1)b^(1 - -4)
2c/ab^5

Now multiply simplified term 1 times simplified term 2:
1/4a^2b^5 * 2c/ab^5
(1 * 2c)/(4a^2b^5 * ab^5)
2c/4a^(2 + 1)b^(5 + 5)
2c/4a^3b^10
2/4 = 1/2, so we have:
c/2a^3b^10