1. The problem is to find the fraction that completes the equation $$4 \frac{1}{6} = 4 \frac{\Box}{\Box}$$. 2. We start by understanding that $$4 \frac{1}{6}$$ is a mixed number, which means 4 whole parts and a fraction $$\frac{1}{6}$$. 3. The equation shows the whole number 4 and a fraction with unknown numerator and denominator represented by the squares. 4. Since the whole number part is the same (4), the fraction $$\frac{\Box}{\Box}$$ must be equal to $$\frac{1}{6}$$. 5. Therefore, the numerator and denominator in the squares are 1 and 6 respectively. 6. So, $$4 \frac{1}{6} = 4 \frac{1}{6}$$. Final answer: $$\boxed{1}$$ for the numerator and $$\boxed{6}$$ for the denominator.