1. The problem is to evaluate the expression $2 : 6 : 3$. 2. The colon symbol ":" is often used to denote division or ratio. Here, we interpret it as division from left to right. 3. So, the expression means $2 \div 6 \div 3$. 4. According to the order of operations, division is performed from left to right. 5. First, calculate $2 \div 6 = \frac{2}{6} = \frac{1}{3}$. 6. Next, divide the result by 3: $\frac{1}{3} \div 3 = \frac{1}{3} \times \frac{1}{3} = \frac{1}{9}$. 7. Therefore, the value of $2 : 6 : 3$ is $\frac{1}{9}$. 8. Final answer: $$\boxed{\frac{1}{9}}$$