1. The problem is to find the value of $\frac{1}{2}$ divided by 6. 2. Recall that dividing by a number is the same as multiplying by its reciprocal. So, dividing by 6 is the same as multiplying by $\frac{1}{6}$. 3. Write the expression as a multiplication: $$\frac{1}{2} \div 6 = \frac{1}{2} \times \frac{1}{6}$$ 4. Multiply the numerators and denominators: $$\frac{1 \times 1}{2 \times 6} = \frac{1}{12}$$ 5. Therefore, the final answer is: $$\boxed{\frac{1}{12}}$$