X:3=564:4

To solve the proportion \( \frac{x}{3} = \frac{564}{4} \), you can cross-multiply:

\[ x \cdot 4 = 3 \cdot 564 \]

Calculating the right side:

\[ 3 \cdot 564 = 1692 \]

Now we have:

\[ 4x = 1692 \]

To find \( x \), divide both sides by 4:

\[ x = \frac{1692}{4} = 423 \]

Thus, \( x = 423 \).