1. The problem is to simplify the expression $\frac{2\sqrt{3} - 3\sqrt{2}}{6}$.\n\n2. The formula used here is to simplify fractions by dividing numerator and denominator by common factors if possible.\n\n3. First, write the expression clearly: $$\frac{2\sqrt{3} - 3\sqrt{2}}{6}$$\n\n4. Check if numerator and denominator have any common factors. The denominator is 6, and numerator terms are $2\sqrt{3}$ and $3\sqrt{2}$. The coefficients 2 and 3 do not share a common factor with 6 other than 1, so no common factor to cancel.\n\n5. We can split the fraction into two parts: $$\frac{2\sqrt{3}}{6} - \frac{3\sqrt{2}}{6}$$\n\n6. Simplify each fraction separately by dividing numerator and denominator by their common factors:\n$$\frac{\cancel{2}\sqrt{3}}{\cancel{6}3} - \frac{\cancel{3}\sqrt{2}}{\cancel{6}2} = \frac{\sqrt{3}}{3} - \frac{\sqrt{2}}{2}$$\n\n7. So the simplified form is $$\frac{\sqrt{3}}{3} - \frac{\sqrt{2}}{2}$$\n\nThis is the simplest exact form of the expression.