To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $6$ and $9$ is $18$. Multiply $\frac{x^{4}}{6}$ times $\frac{3}{3}$. Multiply $\frac{x^{3}}{9}$ times $\frac{2}{2}$.
$$\frac{3x^{4}}{18}-\frac{2x^{3}}{18}$$
Since $\frac{3x^{4}}{18}$ and $\frac{2x^{3}}{18}$ have the same denominator, subtract them by subtracting their numerators.
