1. **State the problem:** We need to find how many thirds are in the mixed number $6 \frac{1}{3}$. 2. **Convert the mixed number to an improper fraction:** $$6 \frac{1}{3} = \frac{6 \times 3 + 1}{3} = \frac{18 + 1}{3} = \frac{19}{3}$$ 3. **Understand the question:** "How many thirds" means how many times $\frac{1}{3}$ fits into $\frac{19}{3}$. 4. **Divide the improper fraction by $\frac{1}{3}$:** $$\frac{19}{3} \div \frac{1}{3} = \frac{19}{3} \times \frac{3}{1} = 19$$ 5. **Interpretation:** There are 19 thirds in $6 \frac{1}{3}$.