Let's simplify the given expression: \(\frac{\sqrt{16x^4 - 72x^2y^2 + 81y^4}}{\sqrt{4x^2 - 12xy + 9y^2}} - (2x - 3y)\).

First, consider the numerator: \(\sqrt{16x^4 - 72x^2y^2 + 81y^4}\).

This expression can be rewritten in the form of a square:

\(16x^4 - 72x^2y^2 + 81y^4 = (4x^2 - 9y^2)^2\)

Therefore, we have:

\(\sqrt{(4x^2 - 9y^2)^2} = |4x^2 - 9y^2|\)

Given that \(2x > 3y\), we know that \(4x^2 - 9y^2 \geq 0\), so \(|4x^2 - 9y^2| = 4x^2 - 9y^2\).

Now consider the denominator: \(\sqrt{4x^2 - 12xy + 9y^2}\). This expression can be simplified to:

\(4x^2 - 12xy + 9y^2 = (2x - 3y)^2\)

Hence:

\(\sqrt{(2x - 3y)^2} = |2x - 3y|\)

Given \(2x > 3y\), we have \(|2x - 3y| = 2x - 3y\).

Substituting back into the main expression, we have:

\(\frac{4x^2 - 9y^2}{2x - 3y} - (2x - 3y)\)

Which simplifies to:

\(\underset{}{} = \frac{(2x - 3y)(2x + 3y)}{2x - 3y} - (2x - 3y)\)\)

Since \(2x - 3y \neq 0\):

\(\underset{}{} = 2x + 3y - (2x - 3y) = 2x + 3y - 2x + 3y\)\)

This results in:

\(6y\)

Thus, the simplified form of the expression is \(6y\). The correct option is:

6y