1. **State the problem:** We have $\frac{2}{3}$ of a yard of ribbon, and we want to cut it into pieces each $\frac{1}{6}$ yard long. We need to find how many pieces we get. 2. **Formula used:** To find the number of pieces, divide the total length by the length of each piece: $$\text{Number of pieces} = \frac{\text{Total length}}{\text{Length of each piece}}$$ 3. **Apply the values:** $$\frac{2}{3} \div \frac{1}{6}$$ 4. **Division of fractions rule:** Dividing by a fraction is the same as multiplying by its reciprocal: $$\frac{2}{3} \times \frac{6}{1}$$ 5. **Multiply numerators and denominators:** $$\frac{2 \times 6}{3 \times 1} = \frac{12}{3}$$ 6. **Simplify the fraction:** $$\frac{\cancel{12}^{4}}{\cancel{3}^{1}} = 4$$ 7. **Answer:** There are 4 pieces of ribbon, each $\frac{1}{6}$ yard long, cut from $\frac{2}{3}$ yard of ribbon.