24m³ ÷ (8m x 2m²)

When multiplying terms with the same base, add their exponents.

$$(8m^6 \times 2m^5) = (8 \times 2) \times (m^6 \times m^5) = 16m^{6+5} = 16m^{11}$$

The expression becomes $(24m^{10}) \div (16m^{11})$.
This can be written as a fraction:

$$\frac{24m^{10}}{16m^{11}}$$

Divide the numerical coefficients:

$$\frac{24}{16} = \frac{3 \times 8}{2 \times 8} = \frac{3}{2}$$

Divide the variable terms using the rule $\frac{a^x}{a^y} = a^{x-y}$:

$$\frac{m^{10}}{m^{11}} = m^{10-11} = m^{-1} = \frac{1}{m}$$

$$\frac{3}{2} \times \frac{1}{m} = \frac{3}{2m}$$

The final answer is $\frac{3}{2m}$.