To add the fractions \( \frac{4}{6} \) and \( \frac{1}{12} \), you first need to find a common denominator.
The least common multiple (LCM) of 6 and 12 is 12.
Now, convert \( \frac{4}{6} \) to have a denominator of 12:
\[ \frac{4}{6} = \frac{4 \times 2}{6 \times 2} = \frac{8}{12} \]
Now, add \( \frac{8}{12} \) and \( \frac{1}{12} \):
\[ \frac{8}{12} + \frac{1}{12} = \frac{8 + 1}{12} = \frac{9}{12} \]
Next, simplify \( \frac{9}{12} \) by dividing both the numerator and denominator by their greatest common divisor, which is 3:
\[ \frac{9 \div 3}{12 \div 3} = \frac{3}{4} \]
Thus, \( \frac{4}{6} + \frac{1}{12} = \frac{3}{4} \).