1. The problem asks how many cups of butter Rama should use to make 3/4 of the cookie recipe, which requires 2/3 cup of butter. 2. To find this, we need to calculate 3/4 of 2/3, which means multiplying the fractions: $$\frac{3}{4} \times \frac{2}{3}$$. 3. Multiply the numerators: $$3 \times 2 = 6$$. 4. Multiply the denominators: $$4 \times 3 = 12$$. 5. So, $$\frac{3}{4} \times \frac{2}{3} = \frac{6}{12}$$. 6. Simplify $$\frac{6}{12}$$ by dividing numerator and denominator by 6: $$\frac{6 \div 6}{12 \div 6} = \frac{1}{2}$$. 7. Therefore, Rama should use $$\frac{1}{2}$$ cup of butter to make 3/4 of the recipe. 8. The correct answer is choice J: 1/2 c.