a) 27y^3

b) 125y^3

c) 216y^3

d) 729y^3

correct answer is: c) 216y^3

Formula use: \left(x-y\right)^3=x^3-y^3-3.x.y\left(x-y\right)

Explanation

Here, given expression is :
\left(2x+3y\right)^3-\left(2x-3y\right)^3-18y\left(4x^2-9y^2\right)
Now, Simplify the expression :
\left(2x+3y\right)^3-\left(2x-3y\right)^3-18y\left(4x^2-9y^2\right)
\rightarrow\left(2x+3y\right)^3-\left(2x-3y\right)^3-3.6y\left(4x^2-9y^2\right)
Now,
\{\left(2x+3y\right)-\left(2x-3y\right)\}=6y
And,
\{\left(2x+3y\right)\times\left(2x-3y\right)\}=\left(4x^2-9y^2\right)
So that, we get :
\left(2x+3y\right)^3-\left(2x+3y\right)^3-3.\{\left(2x+3y\right)\times\left(2x-3y\right)\}.\{\left(2x+3y\right)-\left(2x-3y\right)\}
\rightarrow\{\left(2x+3y\right)-\left(2x-3y\right)\}^3
\rightarrow\left(2x+3y-2x+3y\right)^3
\rightarrow\left(6y\right)^3
\therefore 216y^3
Ans: 216y^3\ .