1. **State the problem:** Convert 12 3/4 quarts (qt) to cups (c). 2. **Formula and rules:** 1 quart = 4 cups. 3. **Convert the mixed number to an improper fraction:** $$12 \frac{3}{4} = \frac{12 \times 4 + 3}{4} = \frac{48 + 3}{4} = \frac{51}{4}$$ 4. **Multiply by the conversion factor:** $$\frac{51}{4} \text{ qt} \times 4 \frac{\text{cups}}{\text{qt}} = \frac{51}{4} \times 4 = \cancel{\frac{51}{\cancel{4}}} \times \cancel{4} = 51 \text{ cups}$$ 5. **Answer:** 12 3/4 quarts equals 51 cups. The correct choice is 51 c.