b. \( \frac{7}{6}: \frac{4}{15}=\frac{35}{12}: x \)

To solve the proportion \( \frac{7}{6}: \frac{4}{15}=\frac{35}{12}: x \), we can rewrite it in a more manageable form. Cross-multiplying gives us \( \frac{7}{6} \cdot x = \frac{4}{15} \cdot \frac{35}{12} \). Calculating the right side, \( \frac{4 \cdot 35}{15 \cdot 12} = \frac{140}{180} \). Simplifying \( \frac{140}{180} \) results in \( \frac{7}{9} \). So, we have \( \frac{7}{6} \cdot x = \frac{7}{9} \). Dividing both sides by \( \frac{7}{6} \) gives \( x = \frac{7}{9} \cdot \frac{6}{7} \). The \( 7 \) cancels out, and we find \( x = \frac{6}{9} \), which simplifies to \( \frac{2}{3} \). Thus, the solution for \( x \) is \( \frac{2}{3} \).