The product of two rational numbers is $-7\dfrac{2}{3}$. If one of them is $3\dfrac{5}{6}$, the other number is:

1. 3
2. -3
3. 2
4. -2

Let the number be $x$.

$3\dfrac{5}{6} \times x = -7\dfrac{2}{3}\\[1em] ⇒ \dfrac{23}{6} \times x = -\dfrac{23}{3}\\[1em] ⇒ x = -\dfrac{23}{3} ÷ \dfrac{23}{6}\\[1em] ⇒ x = -\dfrac{23}{3} \times \dfrac{6}{23}\\[1em] ⇒ x = -\dfrac{23 \times 6}{3 \times 23}\\[1em] ⇒ x = -\dfrac{23 \times 6}{3 \times 23}\\[1em] ⇒ x = -\dfrac{138}{69}\\[1em] ⇒ x = -2$

Hence, Option 4 is the correct option.