The smallest of the fractions $\dfrac{3}{5}, \dfrac{5}{6}, \dfrac{7}{10}, \dfrac{2}{3}$ is

1. $\dfrac{2}{3}$

2. $\dfrac{3}{5}$

3. $\dfrac{5}{6}$

4. $\dfrac{7}{10}$

Given fractions: $\dfrac{3}{5}, \dfrac{5}{6}, \dfrac{7}{10}, \dfrac{2}{3}$

LCM of the denominators (5, 6, 10, 3) = 30

$\Rightarrow \dfrac{3 \times 6}{5 \times 6}, \dfrac{5 \times 5}{6 \times 5}, \dfrac{7 \times 3}{10 \times 3}, \dfrac{2 \times 10}{3 \times 10}\\[1em] \Rightarrow \dfrac{18}{30}, \dfrac{25}{30}, \dfrac{21}{30}, \dfrac{20}{30}$

Among fractions with the same denominator, the one with the smaller numerator is smaller.

So, $\dfrac{18}{30} \lt \dfrac{20}{30} \lt \dfrac{21}{30} \lt \dfrac{25}{30}$

$\dfrac{3}{5} \lt \dfrac{2}{3} \lt \dfrac{7}{10} \lt \dfrac{5}{6}$

Hence, option 2 is the correct option.