Let's work with the mixed numbers:
We have two mixed numbers: $$4 \frac{6}{11}$$ and $$10 \frac{1}{3}$$.
Let's convert them into improper fractions:
1. Convert $$4 \frac{6}{11}$$ to an improper fraction:
$$4 \frac{6}{11} = \frac{4 \times 11 + 6}{11} = \frac{44 + 6}{11} = \frac{50}{11}$$
2. Convert $$10 \frac{1}{3}$$ to an improper fraction:
$$10 \frac{1}{3} = \frac{10 \times 3 + 1}{3} = \frac{30 + 1}{3} = \frac{31}{3}$$
So, the improper fractions are $$\frac{50}{11}$$ and $$\frac{31}{3}$$.
Without a specified operation, we can only convert the mixed numbers to improper fractions.
Converted improper fractions: $$\frac{50}{11}$$, $$\frac{31}{3}$$