Write the proportion equation

Given the proportion $9.6: 16.8:: 18: x$, we use the fundamental property of proportions that the product of the extremes equals the product of the means: $\text{Product of extremes} = \text{Product of means}$.

$9.6 \times x = 16.8 \times 18$

Isolate x

Divide both sides by $9.6$ to solve for $x$: $x = \frac{16.8 \times 18}{9.6}$.

$x = \frac{16.8 \times 18}{9.6}$

Simplify and calculate

Multiply the numerator and denominator by $10$ to eliminate decimals: $x = \frac{168 \times 18}{96}$. Simplifying by dividing $168$ and $96$ gives $7$ and $4$, so $x = \frac{7 \times 18}{4} = \frac{126}{4} = 31.5$.

$x = 31.5$