To simplify this expression, we will distribute the terms in the second parentheses to each term in the first parentheses.

First, distribute 1/2y to each term in the first parentheses:

1/2y 1/4y^2 = 1/8y^3
1/2y yz = 1/2y^2z
1/2y * 4z^2 = 2yz^2

Next, distribute -2z to each term in the first parentheses:

-2z 1/4y^2 = -1/2y^2z
-2z yz = -2yz^2
-2z * 4z^2 = -8z^3

Now, combine the terms:

(1/8y^3 + 1/2y^2z + 2yz^2) + (-1/2y^2z - 2yz^2 - 8z^3)

Simplify by combining like terms:

1/8y^3 - 1/2y^2z + 1/8y^3 - 2yz^2 - 8z^3

2/8y^3 - 1/2y^2z - 2yz^2 - 8z^3

1/4y^3 - 1/2y^2z - 2yz^2 - 8z^3

Therefore, the simplified expression is 1/4y^3 - 1/2y^2z - 2yz^2 - 8z^3.