If \(\frac{a}{c} = \frac{3}{2}\), then we can also conclude that their reciprocals are equal.

In other words: \(\frac{c}{a} = \frac{2}{3}\)

At this point we have two equations: \(\frac{a}{b} = \frac{4}{3}\) and \(\frac{c}{a} = \frac{2}{3}\)

When we multiply the two equations we get: \((\frac{a}{b})(\frac{c}{a}) = (\frac{4}{3})(\frac{2}{3})\)

Simplify: \(\frac{ac}{ba} = \frac{8}{9}\)

Simplify: \(\frac{c}{b} = \frac{8}{9}\)

Answer: \(\frac{8}{9}\)