1. **State the problem:** A cooler contains $6 \frac{3}{4}$ liters of water. A team drinks $\frac{2}{3}$ of the water. We need to find how many liters the team drinks. 2. **Convert mixed number to improper fraction:** $$6 \frac{3}{4} = \frac{6 \times 4 + 3}{4} = \frac{24 + 3}{4} = \frac{27}{4}$$ 3. **Set up the multiplication to find the amount drunk:** The team drinks $\frac{2}{3}$ of $\frac{27}{4}$ liters, so: $$\frac{2}{3} \times \frac{27}{4}$$ 4. **Multiply the fractions:** $$\frac{2 \times 27}{3 \times 4} = \frac{54}{12}$$ 5. **Simplify the fraction:** Divide numerator and denominator by 6: $$\frac{\cancel{54}^{9}}{\cancel{12}^{2}} = \frac{9}{2}$$ 6. **Convert improper fraction to mixed number:** $$\frac{9}{2} = 4 \frac{1}{2}$$ 7. **Answer:** The team drinks $4 \frac{1}{2}$ liters of water. **Number placement:** - Whole number box: 4 - Fraction numerator box: 1 - Fraction denominator box: 2