1. The problem is to evaluate the expression $2 : 6 : 3$ which represents division in sequence. 2. Division is performed from left to right, so we first calculate $2 : 6$ and then divide the result by $3$. 3. Calculate the first division: $$2 : 6 = \frac{2}{6} = \frac{\cancel{2}}{\cancel{6}} = \frac{1}{3}$$ 4. Now divide the result by 3: $$\frac{1}{3} : 3 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$$ 5. Therefore, the value of $2 : 6 : 3$ is $\frac{1}{9}$.