To simplify these expressions, we'll apply the rules of algebra and polynomial division.

a)

Given:
\[
[(2x+y)^3 - 3x(2x+y)^2 - 4(2x+y)] \div (2x+y)
\]

Factor out \((2x+y)\) from each term:
\[
(2x+y)((2x+y)^2 - 3x(2x+y) - 4) \div (2x+y)
\]

Cancel \((2x+y)\):
\[
(2x+y)^2 - 3x(2x+y) - 4
\]

b)

Given:
\[
\left(4x^5y^4 - 6x^4y^5 - \frac{1}{3}x^3y \right) \div 2x^2y^3
\]

Divide each term by \(2x^2y^3\):

1. \(4x^5y^4 \div 2x^2y^3 = 2x^3y\)
2. \(-6x^4y^5 \div 2x^2y^3 = -3x^2y^2\)
3. \(-\frac{1}{3}x^3y \div 2x^2y^3 = -\frac{1}{6}xy^{-2}\)

Result:
\[
2x^3y - 3x^2y^2 - \frac{1}{6}xy^{-2}
\]

c)

Given:
\[
[4(3x+1)^4 - 5(3x+1)^3 + 10(3x+1)^2] \div 3(3x+1)^2
\]

Factor out \( (3x+1)^2 \) from each term:
\[
(3x+1)^2 \left( 4(3x+1)^2 - 5(3x+1) + 10 \right) \div 3(3x+1)^2
\]

Cancel \( (3x+1)^2 \):
\[
\frac{4(3x+1)^2 - 5(3x+1) + 10}{3}
\]

d)

Given:
\[
\left( \frac{1}{2}x^5y^2z^5 - 2x^4y^6z - \frac{3}{4}x^4y^4z^6 \right) \div (-3x^3y^3z^3)
\]

Divide each term by \(-3x^3y^3z^3\):

1. \(\frac{1}{2}x^5y^2z^5 \div -3x^3y^3z^3 = -\frac{1}{6}x^2yz^2\)
2. \(-2x^4y^6z \div -3x^3y^3z^3 = \frac{2}{3}xy^3z^{-2}\)
3. \(-\frac{3}{4}x^4y^4z^6 \div -3x^3y^3z^3 = \frac{1}{4}xyz^3\)

Result:
\[
-\frac{1}{6}x^2yz^2 + \frac{2}{3}xy^3z^{-2} + \frac{1}{4}xyz^3
\]