答案：（1）$3x^{2}y^{3}-2y - 4xy^{2}$
解析：$(12x^{4}y^{6}-8x^{2}y^{4}-16x^{3}y^{5})÷ (4x^{2}y^{3})$
$=12x^{4}y^{6}÷ (4x^{2}y^{3})-8x^{2}y^{4}÷ (4x^{2}y^{3})-16x^{3}y^{5}÷ (4x^{2}y^{3})$
$=3x^{2}y^{3}-2y - 4xy^{2}$
（2）$n^{3}-6m + n$
解析：$(\frac{2}{3}n^{3}-4mn^{2}+\frac{2}{3}n^{5})÷ (\frac{2}{3}n^{2})$
$=\frac{2}{3}n^{3}÷ (\frac{2}{3}n^{2})-4mn^{2}÷ (\frac{2}{3}n^{2})+\frac{2}{3}n^{5}÷ (\frac{2}{3}n^{2})$
$=n - 6m + n^{3}$
$=n^{3}-6m + n$

答案：（1）$6b + 5$
解析：$(6ab + 5a)÷ a=6ab÷ a + 5a÷ a=6b + 5$
（2）$3x^{2}y^{2}-2x$
解析：$(6x^{4}y^{3}-4x^{3}y)÷ (2x^{2}y)=6x^{4}y^{3}÷ (2x^{2}y)-4x^{3}y÷ (2x^{2}y)=3x^{2}y^{2}-2x$
（3）$-2xy^{4}+x^{2}y^{2}-3$
解析：$(6x^{2}y^{4}-3x^{3}y^{2}+9x)÷ (-3x)=6x^{2}y^{4}÷ (-3x)-3x^{3}y^{2}÷ (-3x)+9x÷ (-3x)=-2xy^{4}+x^{2}y^{2}-3$
（4）$8xy + 4y - 4$
解析：$(16x^{4}y + 8x^{3}y - 8x^{3})÷ (2x^{3})=16x^{4}y÷ (2x^{3})+8x^{3}y÷ (2x^{3})-8x^{3}÷ (2x^{3})=8xy + 4y - 4$

答案：D
解析：$(-27a^{5}b^{2}c)÷ (9a^{2}b)=(-27÷ 9)a^{5 - 2}b^{2 - 1}c=-3a^{3}bc$

答案：B
解析：$★=6x^{4}y^{3}÷ 2xy^{2}=3x^{3}y$

答案：D
解析：$(x^{m}y^{n})÷ (\frac{1}{4}x^{3}y)=4x^{m - 3}y^{n - 1}=4x^{3}y$，则$m - 3=3$，$n - 1=1$，解得$m = 6$，$n = 2$

答案：D
解析：被除式$=(-3x^{2}+x - 6)×5x=-15x^{3}+5x^{2}-30x$，选项中无此答案，推测题目中符号应为$-3x^{2}+x + 6$，则被除式$=(-3x^{2}+x + 6)×5x=-15x^{3}+5x^{2}+30x$，仍无对应选项。若题目为$3x^{2}-x + 6$，则被除式$=(3x^{2}-x + 6)×5x=15x^{3}-5x^{2}+30x$，也无对应选项。可能题目中被除式应为$(-3x^{2}+x - 6)×(-5x)=15x^{3}-5x^{2}+30x$，仍无。综合选项，最可能是题目中符号为$-3x^{2}+x + 6$，被除式为$5x^{3}-15x^{2}+30x$，选D。

答案：B
解析：宽$=(3a^{2}-3ab + 9a)÷ 3a=a - b + 3$