To multiply the fractions \( \frac{1}{2} \) and \( \frac{4}{6} \), you multiply the numerators and the denominators:
\[ \frac{1 \times 4}{2 \times 6} = \frac{4}{12} \]
Now, we can simplify \( \frac{4}{12} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 4:
\[ \frac{4 \div 4}{12 \div 4} = \frac{1}{3} \]
However, from the options you provided:
- 1/12
- 6/12
- 16/12
- 4/12
The correct answer is \( \frac{4}{12} \).