To find out how much flour the baker should use with 2 cups of sugar, we can set up a ratio based on the original recipe.
The original ratio of sugar to flour is:
\[ \frac{3 \text{ cups of sugar}}{4 \text{ cups of flour}} = \frac{2 \text{ cups of sugar}}{x \text{ cups of flour}} \]
Cross-multiply to solve for \(x\):
\[ 3x = 4 \cdot 2 \]
\[ 3x = 8 \]
Now, divide both sides by 3:
\[ x = \frac{8}{3} \]
So, the baker should use \(\frac{8}{3}\) cups of flour, which is approximately 2.67 cups of flour.