Given data

• Molality of KOH solution: $m = 6.50\ \text{mol kg}^{-1}$
• Density of solution: $\rho = 1.89\ \text{g cm}^{-3}$
• Molar mass of KOH: $M_{\text{KOH}} = 39 + 16 + 1 = 56\ \text{g mol}^{-1}$

Take 1 kg of solvent Since molality is defined as moles of solute per kg of solvent, for $1\ \text{kg}$ water: $\text{moles of KOH} = 6.50$

Mass of solute $\text{mass of KOH} = 6.50 \times 56 = 364\ \text{g}$

Total mass of solution $\text{mass of solution} = 1000 + 364 = 1364\ \text{g}$

Volume of solution using density $\text{Volume} = \frac{\text{mass}}{\text{density}} = \frac{1364}{1.89} = 721.69\ \text{cm}^3$ Convert to dm$^3$ (or L): $721.69\ \text{cm}^3 = 0.72169\ \text{dm}^3$

Calculate molarity $\text{Molarity} = \frac{\text{moles of solute}}{\text{volume of solution in dm}^3}$ $M = \frac{6.50}{0.72169} \approx 9.01\ \text{mol dm}^{-3}$

Nearest integer $\boxed{9}$

Comparison with stored answer Stored correct answer = $9$

Our derived answer also is $9$, so they agree.