To simplify the given fraction \(\frac{2\sqrt{3} - \sqrt{2}}{\sqrt{3} + 2\sqrt{2}}\), we can use the conjugate rule to rationalize the denominator. The conjugate of the denominator \(\sqrt{3} + 2\sqrt{2}\) is \(\sqrt{3} - 2\sqrt{2}\).

Multiply both the numerator and denominator by the conjugate of the denominator:

\[\frac{2\sqrt{3} - \sqrt{2}}{\sqrt{3} + 2\sqrt{2}} \cdot \frac{\sqrt{3} - 2\sqrt{2}}{\sqrt{3} - 2\sqrt{2}}\]

Simplify each term:

\[\frac{(2\sqrt{3})(\sqrt{3}) - (2\sqrt{3})(2\sqrt{2}) - (\sqrt{2})(\sqrt{3}) + (\sqrt{2})(2\sqrt{2})}{(\sqrt{3})(\sqrt{3}) - (2\sqrt{2})(2\sqrt{2})}\]

\[\frac{6 - 4\sqrt{6} - \sqrt{6} + 4}{3 - 8}\]

\[\frac{10 - 5\sqrt{6}}{-5}\]

Divide both the numerator and denominator by -5:

\[\frac{-10 + 5\sqrt{6}}{5}\]

Now, we can separate this fraction into the sum of two terms:

\[\frac{-10}{5} + \frac{5\sqrt{6}}{5}\]

\[-2 + \sqrt{6}\]

So, the given fraction is equal to \(-2 + \sqrt{6}\), which means \(m = -2\) and \(n = 1\).

The correct answer is:

B. -2, 1