Ratio, Rate, and Proportion: Finding Unknown Ratios

$\dfrac{2}{3} = \dfrac{6}{N} \quad \implies \quad N = \dfrac{3}{2} \times 6 = \boxed{9}$

$2 \times 3 = 6$

$3 \times 3 = \fbox 9$

Converting both of them into fractions, the ratio 2 to 3 is equal to $\frac{2}{3}$ and the ratio $6 : N$ is equal to $\frac{6}{N}$ . Hence, we want $\frac{2}{3} = \frac{6}{N}$ , or that $N = \frac{ 3 \times 6}{2} = 9$ .